After asking the question, I looked at an old copy of "Requiem" in an anthology that was printed during the time span when McIntyre and Charlie were born, but is now getting closer to Harriman's age in "Requiem" every year and every decade. And I found some clues to the date.
Harriman has a memory from when he was about 17:
"Son, I want to have a little serious talk with you."
I know you had hoped to go to college next year" -- Hoped! He had lived for it. The University of Chicago to study under Moulton, then on to the Yerkes Observatory to work under the eye of Dr. Frost himself...
Edwin Brant Frost was director of the Yerkes Observatory from 1905 to 1932, and Harriman should have been 17 sometime during that period if he expected to work under Frost in 5 years, thus putting his birth sometime between about 1888 and about 1915.
Forrest Ray Moulton (1872-1952) was Professor of Astronomy at the University of Chicago from 1896 to 1926. So Harriman should have been 17 and expecting to study Astronomy under Moulton at the University of Chicago sometime between 1896 and 1926, and thus been born about 1879 to 1909.
So together they indicate that Harriman was born between about 1888 and about 1909, and would turn 70 between 1958 and 1979, 80 between 1968 and 1989, 90 between 1978 and 1999, and 100 between 1988 and 2009.
Another dream memory:
There was that time--oh, yes, 1910--a little boy on a warm spring night.
"What's that, daddy?"
"That's Halley's Comet, sonny."
Where did it come from?"
I don't know. son. From way out in the sky somewhere."
"It's beyooootiful, daddy. I want to touch it."
"'Fraid not, son."
Halley's Comet did become visible to the naked eye about 10 April 1910, and so fits the warm spring night better than the Great Daylight Comet of 1910 which was seen in January.
So in 1910 Harriman was old enough to talk in short sentences, but young enough to not know that celestial bodies are out of reach. I guess Harriman should have been at least 3 years old but not much older, so he should have been born about 1904 to 1907, I guess.
So Harriman should have turned 70 about 1974 to 1977, 80 about 1984 to 1987, 90 about 1994 to 1997, and 100 about 2004 to 2007.
When talking with McIntryre and Charlie, Harriman says:
"You young fellows have grown up to rocket travel the way I grew up to aviation. I'm a great deal older than you are, maybe fifty years older. When I was a kid practically nobody believed that men would ever reach the Moon. You've seen rockets all your lives, and the first to reach the Moon got there before you were old enough to vote. When I was a boy they laughed at the idea.
So Harriman might be 45 to 55 years older than McIntyre and Charlie, thus making them born about 1949 to 1962, or maybe he might be 40 to 60 years older than them, making them born about 1944 to 1967. Harriman thinks that the first manned Moon landing was before they were old enough to vote at age 21, so the first lunar landing should have been by 1970 to 1983, or maybe by 1965 to 1988.
McIntyre and Charlie seem like they are probably between about 25 and about 40 years old. So that would make the date of "Requiem" about 1974 to 2002, or maybe about 1969 to 2007.
At one point Harriman says:
It was exciting, Charlie. This has been a wonderful, romantic century, for all of its bad points. And it's grown more wonderful and more exciting every year..."
And I doubt if Harriman would speak that way about the 21st century if he had only lived a few years in it. So that seems like the latest possible year for "Requiem" would be 2000.
So "Requiem" would probably happen about 1969 to 2000, with Harriman aged about 62 to 96, and probably somewhere near the middle of that timespan.
Spencer's comment says that there is a statement that the first Moon landing in The Man Who Sold the Moon happens in 1978.
And it certainly took a number of years for Luna City to develop as much as it seems to have in "Requiem". So 5 years later would be in 1983, 10 years later would be in 1988, 15 years later would be in 1993, and 20 years later would be in 1998.
After Harriman tells McIntyre and Charles that when he was a boy people laughed at the idea of going to the Moon.
"But I believed-- believed. I read Verne and Wells and Smith, and I believed that we could do--that we would do it. I seat my on being one of the men to walk thesurface of the Moon, to see her side, and to look back on the face of the Earth, hanging in the sky."
"I used to go without my lunches to pay my dues in the American Rocket Society, because I wante to believe that I was helping to bring the day nearer when we would reach the Moon. I was already an old Man when that day arrived.
So Harriman was old enough to pay for his lunches when he was a member of the American Rocket Society. The American Interplanetary Society was founded April 4, 1930, and changed its name to the Amerian Rocket Society April 6, 1934. I think that means that Harriman should have been at least 18 and working sometime in or after 1934.
Anyway, Harriman doesn't specify his age as a child or an adult when he read Verne and Wells and Smith. He could have started reading Verne and Wells as a boy sometime in the 1910s. But - at least in our timeline - The first published work by E.E. Smith, The Skylark of Space, was first published in Amazing Stories, August to October, 1928, when Harriman should have been an adult or close to it.
The Skylark of Space was also the first Smith novel to be published as a book, in 1946, in the future when Heinlein wrote "Requiem". So Heinlein pictured Harriman reading science fiction pulp magazines, even when he was an adult (one of the flashbacks has Harriman's business partner criticizing him for it), and in our timeline the first one was Amazing Stories in April, 1926.
At one point Harriman says:
I wasn't unusual; there were lots of boys like me--radio hams they were, and telescope builders, and airplane amateurs. We had science clubs, and basement laboratories, and science-fiction leagues--the kind of boys who thought there was more romance in one issue of the Electrical Experimenter than in all the books Dumas ever wrote.
If Harriman was not yet 21 when he joined some very early science fiction club in 1926, he would have been born in 1905 at the earliest.
Hugo Gernsback founded Modern Electrics magazine in 1908 and changed the name to The Electrical Experimenter in May 1913, and changed the name again to Science and Invention in July 1920, continuing until 1931. The Electrical Experimenter published a few science fiction stories by Gernsback and others, starting in 1915.
So it would have been theoretically possible for Harriman to have joined a science fiction club aged under 21 as early as 1915 and thus have been born in 1894 or later.
If Harriman had to be at least 10 to read The Electrical Experimenter before it changed its title in 1920, he would have been born in 1910 or earlier.
But I think that Harriman's statements about what boys like him were interested in should be taken with a grain of salt. Union Civil War soldiers like to call themselves "the boys in Blue". But most of them were young men in their twenties, with large minorities of older men and of teenage boys, and maybe a few thousand preteen boys.
So I think that Harriman and the other "boys" he spoke of started their scientific interests when preteen or teenage boys, and continued those boyhood imterests as young men in their twenties and thirties and thus figuratively "boys", as well as their responsibilites allowed. That is how many scientists and science fiction writers got into their adult careers.
The most important clue is that Harriman was alive and a little child in 1910, thus making him born a few years before 1910.
I once read that the character of Lessingham in Eric Rucker Eddison's fantasy novels The Worm Ouroboros (1922), MIstress of Mistresses (1935), A Fish Dinner in Memison (1941), and The Mezantian Gate (1958) is the person that Eddison wanted to be and wished he was.
And after finding out yesterday that the short range of years when Harriman should have been born, say 1905 to 1908, included Heinlein's birth date of July 7, 1907, I wonder whether Harriman was a similar alter ego of Heinlein's, someone who Heinlein would want to be. So it is possible that Delos D. Harriman was also born on 07-07-07.
And it that guess was correct, possibly Harriman died on his 80th or 90th birthday, July 7, 1987 or July 7, 1997.
So all that would be necessary to narrow down Harriman's age in "Requiem" further would be a study of all the date clues in the 20th century stories of the Future History series to see when they could happen and thus when "Requiem" could happen.
Added January 08/09 2022. I looked at my copy of The Green Hills of Earth, 1952, 1963, and the timeline of the future history in it.
The year 1975 is beside "The Roads Must Roll" and "Blowups Happen".
"The Man Who Sold The Moon" is a little lower, right above a line that probably marks the year 1980.
The stories between the line that probably marks the year 1980 and the line at 2000 are, in order:
"Delilah and the Space Rigger".
"The Long Watch".
"Gentlemen, Be Seated".
"The Black Pits of Luna".
"Its Great to be Back".
"We Also Walk Dogs".
So according to the order that the stories are listed in that chart, "Requiem" should happen an unspecified period of time before "The Black Pits of Luna". The story titles are printed equal distances apart on succesive lines, with no clue to the relative time spacing between them.
And reading "The Black Pits of Luna" today I noticed a mention of a previous date.
The characters visit the site of a nuclear research labratory on the far side of the Moon, which is now a 20 mile wide crater. The inscription on the monument to the deceased gives the date of the disaster as "the Eleventh Day of August 1984".
So "The Black Pits of Luna" should be some time after "Requiem" and also some time, probably years or decades, after "the Great Disaster of 1984". But it seems uncertain whether "Requiem" was before or after the Great Disaster on August 11, 1984.
Added Jan. 11, 2022.
Here is a another rther vague clue to the ficitonal date of "Requiem".
In "Requiem" a deputy federal mrashall tries to arrest McIntyre, Cummings, and Harriman for "conspiracy to violate the Space Precautionary Act", which obviously must have been enacted before the date of "Requiem". Possibly it was enacted years before, frustating Harriman's previous efforts to get into space.
The Space Precautionary act is mentioned twice in "The Green Hills of Earth.
When Rhysling signs up for the trip on the Goshawk where he is blinded, the narrator says:
The crew signed releases for everything in those days; a Lloyd's associate would have laughed in your face at the notion of insuring a spaceman. The Space Precautionary Act had never been heard of, and the Company was responsible only for wages, if and when. Half the ships that went further than Luna City never came back.
When the now blind Rhysling makes his last voyage, from Venus to Earth, the skipper of the Falcon doesn't want to take him for free, and quotes the Space Prcautionary Act, Clause Six. Rhysling finishes the final form of his song The Green Hills of Earth on that voyage.
The Green Hills of Earth grew thorugh twenty years. The earliest form we know about was composed before Rhysling was blinded, during a drinking bout with some of the indentured men on Venus. The verses were concerned mostly with what the labor clients intended to do back on Earth if and when they ever paid back their bounties and thereby be allowd to go home. Some of the Stanzas were vulger, some were not, but the chorus was recognizably that of Green Hills.
So 20 years allegedly passed between when Rhysling started the first version of The Green Hills of Earth, which was before Rhysling went on thevoyage where he was blinded, which was before the Space Precautionary Act was passed, and the voyage where Rhysling completed The Green Hills of Earth which was after the space Precautionary Act was passed.
The timeline chart of the Future History puts The Green Hills of Earth after the year 2000 and before the year 2025, and probably closer to 2000.
So the Space Precautionary Act should have been passed sometime after 1980 to 2005, and "Requiem" should have happpened sometime after the Space Precautionary Act was passed.
Added Jan. 12/13 2022.
"The Long Watch" opens with a quotation from an editorial "After Ten Years", from the New York Times, 17 June 2009. So the events in "The Long watch" should happen in June, 1999, and that should probably be within a few years of the date of "Requiem".