Getting animal people is very difficult, in my experience. I've had a total of 1 petitioner (a Gorlak, who died of old age after just a few years), and probably less than a dozen animal people visitors.
The crucial factor is that they are such a small part of the world population, so they'll make up but a small part of the worlds traveling visitors. I've tried and failed to get animal people to be present in significant numbers (you can mod them in as regular civs, but I'm not prepared to do that).
If the world doesn't have much population (or most of it is under goblin civ rule) there won't be many visitors to travel around.
Apart from that, temples dedicated to deities open to visitors attract various riffraff, such as peddlers, pilgrims, and monks. Unfortunately, none of that riffraff has any use in the fortress as they never petition. They are said to serve as a pool for spies, though, but apart from that, they gobble up a large portion of the visitor allotment so you get fewer visitors that may petition.
Another side effect of open dedicated temples is that visitors tend to go to these temples for half year long prayer benders before they get to whatever business they're supposed to be on (demand an artifact, petition, research, enjoy themselves, etc.), so visitor turnover is slowed down (and you can achieve the same effect by reducing the visitor cap, while getting fewer units to gobble up your FPS).