The series is about a group of kids being woken up one by one throughout the series after an apocalypse and each kid can do something special (I can't remember if it was magical, but it could have been) and they have to restore humanity. I remember that each kid looked vastly different from each other.
I borrowed these books from my private school library in the 1990's-2003ish time period.
Seven Sleepers Series by Gilbert Morris.
Took place after an apocalypse: Josh Adams, 14, awakes from a 50-year sleep. Ancient prophecy commands him and the other Sleepers to unite in battle against the evil priests, and combat the doubt that threatens their faith.
Children are awoken 1 by 1: Seven sleeping children were preserved in capsules for 50 years, and awoken during the series.
Restoring Humanity: I'm hazy on the exact details, but as a Christian Post-Apocalyptic Sci-Fi series, that's got to be the goal. I don't think that the genre would allow kids to be trying to destroy the universe.
1990-2000: The novels were written from 1994-1997.
Private School Library: Being young-adult Christian novels, they would have only been stocked by private, religious schools, like the one I went to (and rented books from.) They definitely didn't stock Ringworld.
Kids looked vastly different: I'm not sure how this one played into things. I'd have to re-read the series again to know exactly how different each kid looked. There was at least one white boy, one white girl, and from what I barely remember, a few other races.
I hope this helps! I have had the toughest time finding the name of the series again, but I finally found it again.
Per @Thomas' comment, this sounds very strongly like you're describing "Shade's Children" by Garth Nix.
This reminds me of the Avatars series, by Tui T Sutherland. The first book is Avatars: So This is How It Ends, and there are at least three other books in the series: Shadow Falling, The Menagerie, and The Menagerie #2. The first book, at least the edition I saw, was published in 2006, so a couple years later than your time frame.
The basic plot-line has four teens wake up in a post apocalyptic world, about 75 years into their own future. Each kid discovers they now have magical powers, different ones per kid. Humankind is pretty scarce - kids had stopped being born, the only people left were old and knew there was no future generation (at least until teens pop up), and there were also robot monsters and bio-engineered animals running around.
The kids were brought forward in time because
the gods of the major (polytheistic) pantheons - Greek, Egyptian, Meso-American, Hindu, and Polynesian - had chosen the kids as avatars to fight out among themselves which pantheon would be the ultimate gods and have power over the others.
As far as I recall, each kid was a representation of a different historical people, and so were each of a different ethnicity. This would match the point that the kids all looked different.
People had stopped being born (leading to the post-apocalyptic world) because
Humanity was going to be restarted (I think) under the auspices of the winning pantheon - since they had all stopped believing in the gods, in modern times especially, wiping them out and starting over with a civilization completely under their thumb from the start was more convenient or something.
There was definitely an expectation (at least by the aged humans still alive) that the kids, being kids and "clearly" young enough to be from after the point where kids had stopped being born - or at least of reproducing age given that they're teenagers - and thus would somehow fix things and restore humanity. Obviously whether this happens or not is a plot point.
I recall a specific scene where there is a group that has a child, just one, who was born quite late after the cutoff point. The group had a semi-religious belief she was some sort of sign or savior that would restore humanity, even though they were not sure how (she was born incapable of reproduction, and the actual problem was no kids, so no obvious fix). Actually, the whole setup was a joke on one of the pantheon's parts, giving false hope for amusement.
The Chrysalids, first published in 1955 by British writer John Wyndham.
An undetermined number of years into the future, post-apocalypse rural Labrador has become a warmer and more hospitable place than it is at present. The inhabitants of Labrador have vague historical recollections of the "Old People", a technologically advanced civilisation which existed long ago and which they believe was destroyed when God sent "Tribulation" to the world to punish their forebears' sins. The society that has survived in Labrador is loosely reminiscent of the American frontier during the 18th century, with a level of technology in use similar to the Amish of the present-day United States.
....
David and a few other children in the district harbour their own invisible mutation: they have telepathic abilities. The group are initially supported, advised and protected by David's moderate Uncle Axel, who comes to know about the group through some unguarded chattering when David is still small. Uncle Axel goes so far in his protection as to kill the husband of one of the group who was abusing his telepath wife, and about to blackmail the rest of the group.
This reminds me of a Japanese anime movie, Harmagedon: Genma taisen (1983) also known as Harmagedon: The Great Battle with Genma.
From IMDb:
A Transylvanian princess, a Japanese high school student and a 2000 year old warrior are selected to be part of a small force of powerful psionic warriors assembled to be the defenders of Earth against a nihilistic alien entity bent on pure total cosmic destruction.
