Here is a guide on how to find Pettable Animals in Assassin’s Creed IV Black Flag.
Pettable Animals and Where To Find Them
Cats:
Almost everywhere. Normally it’s them petting you though.
Dogs:
Easy to find in small communities. There’s usually some in camps. Textbook petting.
Parrots:
Usually found in front of general stores. The easiest one is in Great Inagua. There’s always a cage so you can only let them nibble your fingers.

Chickens:
A lot in Nassau. Found in villages and suburbs. You can only feed them. Maybe they’re too small to pet.

Cows:
There’s one in Ile à Vache’s tavern. Can’t remember the rest’s whereabouts.Same as chickens maybe. Try your luck.

Goats:
There’s one or two in Great Inagua. Still, can’t remember seeing them elsewhere. Same as cows maybe. Break a leg.

That “thing”:
Activate the “Shiver Me Timbers” cheat and you can see them. Anywhere. Fiery petting.
Almost everywhere. Normally it’s them petting you though.

Easy to find in small communities. There’s usually some in camps. Textbook petting.

Usually found in front of general stores. The easiest one is in Great Inagua. There’s always a cage so you can only let them nibble your fingers.

Chickens:
A lot in Nassau. Found in villages and suburbs. You can only feed them. Maybe they’re too small to pet.

Cows:
There’s one in Ile à Vache’s tavern. Can’t remember the rest’s whereabouts.Same as chickens maybe. Try your luck.

Goats:
There’s one or two in Great Inagua. Still, can’t remember seeing them elsewhere. Same as cows maybe. Break a leg.

That “thing”:
Activate the “Shiver Me Timbers” cheat and you can see them. Anywhere. Fiery petting.

By solidude