I never bothered to go over the coronation because it doesn't affect what ending you get. There was a draft of the game many years ago where doing poorly on the coronation got you a bad ending, but it was cut.
Still, if you really want to know what the best choices are during the coronation:
- Greet Mina first
- Prince Beckett
- Edmund
- Connor
- (If you punched Vidar earlier, admit it but don't apologize for it)
- (If Janine is still alive, you can judge her however you like)