I saw from another thread that you have a GCC. They are an easy size to quickly towel with one hand (using a small hand or dish towel) and pop into their travel cage. Quietly and calmly approach from behind, gently encircle his body with your toweled hand, and in he goes. If you're too slow and he catches on and flies away or panics, have another person nearby. Mark his location visually, have the other person turn out the lights, then proceed with the towel. Birds will tend not to fly in the dark as readily.
The key is really to make sure he's engaged with something, like food, before reaching for him. AND preferably have him in a position where things aren't in the way when toweling him. So feeding him near a perch on an open cage door is a better place than a perch deep inside the cage. It should ideally be so smooth and quick that he doesn't even realize what's happened until he's secure in his travel cage. My GCC can be a nasty beast, and yet he has never been upset about being "magically teleported" into his travel cage! Also make sure to leave yourself plenty of time prior to the appointment so that you don't feel stressed or in a hurry to catch him.