The counter-argument to "it doesn't work" is that the wording or Royal Carriage says
Directly after you finish playing an Action card, if it's still in play, you may call this to replay that Action.
What is unclear to me is if the bold part is part of the trigger condition or the triggered effect. If it is part of the triggered effect, then "it doesn't work" is true. If it is part of the trigger condition, however, then it should work, because both Royal Carriages triggered on a Knight that was in play when its effect ended.
The counter-argument to "it doesn't work" is that the wording or Royal Carriage says
Directly after you finish playing an Action card, if it's still in play, you may call this to replay that Action.
What is unclear to me is if the bold part is part of the trigger condition or the triggered effect. If it is part of the triggered effect, then "it doesn't work" is true. If it is part of the trigger condition, however, then it should work, because both Royal Carriages triggered on a Knight that was in play when its effect ended.
But again, you can only do one thing at a time. You can't call 2 Royal Carriages simultaneously. By the time you're ready to call the 2nd one, the original card is no longer in play, and the trigger no longer applies.