No the rules do not appear to have changed. There doesn't have to be an alternative for the non-obligatory rites of Knighthood. The recepients and the Knight executing the process can simply skip those rites.
###Procedure of Knighthood:
The Knighthood ceremony involves following steps in that order:
- Vigil of a Knight-to-be in a sept for a night. (non-obligatory)
- Anointment of the new Knight by a Septon (non-obligatory)
- Dubbing of the Knight-to-be by an existing Knight.
- Having an audience to witness the dubbing ceremony (non-obligatory)
The non-obligatory steps are customary but aren't required. As long as you are knighted by another Knight, you can proudly call yourself a Ser.
###Knighthood Historically
“Hmpf.” The man Plummer rubbed his nose. “Any knight can make a knight, it is true, though it is more customary to stand a vigil and be anointed by a septon before taking your vows. Were there any witnesses to your dubbing?”
Dunk & Egg: The Hedge Knight
Notice that the Steward in charge of the Tourney at Ashford clearly states that it is customary to have a septon anoint you and an audience to witness the dubbing however he does not say that it is obligatory. As long as a Knight dubs you, you are alright.
Also we have knighting of Ser Glendon Flowers without any anointment by a Septon or a vigil:
"He says he is a knight."
"Oh, that much is true. The boy and his sister grew up in a brothel, called the Pussywillows. After Penny Jenny died, the other whores took care of them and fed the lad the tale his mother had concocted, about him being Fireball's seed. An old squire who lived nearby gave the boy his training, such that it was, in trade for ale and cunt, but being but a squire he could not knight the little bastard. Half a year ago, however, a party of knights chanced upon the brothel and a certain Ser Morgan Dunstable took a drunken fancy to Ser Glendon's sister. As it happens, the sister was still a virgin and Dunstable did not have the price of her maidenhead. So a bargain was struck. Ser Morgan clubbed her brother a knight, right there in the Pussywillows in front of twenty witnesses, and afterwards little sister took him upstairs and let him pluck her flower. And there you are."
Dunk & Egg: The Mystery Knight
Ser Glendon:
- did not stand a vigil.
- did not have a septon anoint him
And yet he was a legal knight because a Knight knighted him.
###Knighthood in modern times
Jaime got knighted without anointment by a septon.
The sept where he'd spent the night was not a third as large as any of the Great Sept's seven transepts. Jaime had laid his sword across the Warrior's knees, piled his armor at his feet, and knelt upon the rough stone floor before the altar. When dawn came his knees were raw and bloody. "All knights must bleed, Jaime," Ser Arthur Dayne had said, when he saw. "Blood is the seal of our devotion." With dawn he tapped him on the shoulder; the pale blade was so sharp that even that light touch cut through Jaime's tunic, so he bled anew. He never felt it. A boy knelt; a knight rose.
A Feast for Crows - Jaime I
Notice that Jaime's knighthood is very recent and he:
- Stood the vigil at the sept
- Was not anointed by a Septon before his dubbing
- Was dubbed by a Knight
Also:
More than six hundred new knights were made that day. They had held their vigil in the Great Sept of Baelor all through the night and crossed the city barefoot that morning to prove their humble hearts. Now they came forward dressed in shifts of undyed wool to receive their knighthoods from the Kingsguard.
A Clash of Kings - Sansa VIII
Notice that these Knights stood their vigils and were dubbed however they were not anointed.
The response by Barristan Selmy and Jorah Mormont is very interesting:
Ser Jorah gave the old man a long look. "A squire with a stick slew Mero of Braavos, is that the way of it?"
"A stick," Dany confirmed, "but no longer a squire. Ser Jorah, it's my wish that Arstan be knighted."
"No."
The loud refusal was surprise enough. Stranger still, it came from both men at once.
A Storm of Swords - Daenerys V
Notice that there is no septon in Daenerys' service Nor did she ask Whitebeard to stand a vigil first but she still thinks that Knighting whitebeard would stick. Jorah Mormont and Whitebeard thought the same and refused.
Also there's unverified account of Ser Osmund's knighthood:
"Who knighted you?"
"Ser Robert . . . Stone. He's dead now, my lord."
"To be sure." Ser Robert Stone might have been some bastard from the Vale, he supposed, selling his sword in the Disputed Lands. On the other hand, he might be no more than a name Ser Osmund cobbled together from a dead king and a castle wall. What was Cersei thinking when she gave this one a white cloak?
A Storm of Swords - Jaime VIII
The only known sept and Septons to be found in Essos, are in Bravos, not in disputed lands. Osmund Kettleblack has confessed that he fought in disputed lands but he never said anything about visiting or serving in Bravos. So most probably, Osmund Kettleblack did not stand a vigil or get anointed prior to getting knighted, if he actually got knighted at all.
###The conclusive argument on modern Knighting ceremonies
The most important bit of evidence is what we see when Beric Dondarrion creates knights without a vigil or a septon to anoint.
A wan smile crossed Lord Beric’s lips. “Thoros, my sword.”
This time the lightning lord did not set the blade afire, but merely laid it light on Gendry’s shoulder. “Gendry, do you swear before the eyes of gods and men to defend those who cannot defend themselves, to protect all women and children, to obey your captains, your liege lord, and your king, to fight bravely when needed and do such other tasks as are laid upon you, however hard or humble or dangerous they may be?”
“I do, m’lord.”
The marcher lord moved the sword from the right shoulder to the left, and said, “Arise Ser Gendry, knight of the hollow hill, and be welcome to our brotherhood.”
A Storm of Swords - Arya VIII
Notice, there is no vigil, no septon to anoint, yet Gendry is a knight. It can be argued that by that time, Beric had converted to faith of the Red God. However notice that in the dubbing, he says gods, not God/Rhllor as the follower of the Red God say.
Even if we assume that the lack of vigil or anointing by a septon is because the Brotherhood had forsaken faith of seven, we see that they did not create alternatives for those religious ceremonies like standing a vigil near fire or getting anointed/blessed by their red priest, Thoros of Myr.
###Anointment by High Septon
Anointment by the highest ranking member of the clergy of the faith is of course very special. The quote about Ser Jorah being anointed by the High Septon is correct however:
- Illyrio may have been wrong.
- The anointment may have been honorary because it has no impact on knighthood.
Evidence for the anointment by the High Septon being inconsequential can be seen here:
He waddled across the yard almost at a run and crowded into the back of the castle sept as Joffrey fastened white silk cloaks about the shoulders of the two newest members of his Kingsguard. The rite seemed to require that everyone stand, so Tyrion saw nothing but a wall of courtly arses. On the other hand, once the new High Septon was finished leading the two knights through their solemn vows and anointing them in the names of the Seven, he would be well positioned to be first out the doors.
A Clash of King - Tyrion XI
The two said members were:
- Ser Balon Swann
- Ser Osmund Kettleblack
Both were knights prior to being inducted in the King's guard yet they are being anointed by High Septon. That means one can be a knight without the anointment given that both men were knights long before they were anointed by High Septon.
Also see:
- Who can knight you so that Knighthood would stick? to learn about different way different character came across their knighthood.
###Ser Jorah's Knighthood
Ser Jorah is said to have won his Knighthood on field of Pyke where Robert Baratheon personally knighted him.
Few things have never been clear.
- Does Jorah follow faith of seven or the Old gods?
- Was High Septon present in Pyke in the battle? If so, why?
- Was the anointment actually performed or is it just a lie or a mistake on part of Illyrio?
- Was the anointment performed prior to Robert dubbing Jorah a knight as customary or afterwards as in the case of Ser Balon Swann?
In any case, Illyrio's account, being a foreigner and less familiar with Westerosi customs, can't be relied upon. There are also Ironborn knights like:
- Ser Aladale Wynch
- Ser Harras Harlaw
It is unclear if they follow the religion of drowned gods or how they got their knighthoods.
###Conclusion
As you can see, during different knighting ceremonies, one or more factors are missing. However, one factor is consistent in all, A knight knighting a knight-to-be. That's the only thing that matters, as the Tale of Dunk & Egg also makes it abundantly clear for us.