I really really wanted to do this with Kiwi, she would be so perfect.
BUT, one of the requirements was that they be declawed, and she is not. So, I wasn't about to declaw her just for that. I offered to put nail guards on her, but that was a no-go.
This was through my local SPCA, they have a pet visitation program. There was no real training involved, it was more about personality. The cat had to be calm, easygoing and friendly with strangers of all sorts. They would also have to be fairly bomb-proof, meaning they wouldn't be scared at strange sights (wheelchairs, IV poles, etc) sounds (from people, medical equipment, etc) or smells (hospital antiseptic, etc.)
Good luck! I've done visitation with my rabbits and dogs and it is such a rewarding experience.