Well, 'tame' is a bit misleading, but they're comfortable enough with humans to behave themselves. If you know how to interact with them, they've been trained to know how to interact with you.
I think I could introduce you to one of my girls. Raksha has the best temperament of the lot. There will be some instructions up-front, but you're familiar with animals, you probably know most of this already.
Rabbits? I've never had one myself, but they seem like they'd make a good pet.