Kind of taking the pack in two directions here - spinoff or similar of domesticated or barnyard animals, and then wilder animals that are commonly found in sections of or zoos themed for children
Shetland Pony
Mandarin Duck
Cottontail Rabbit
Yak
Patagonian Mara
Squirrel Monkey
Coatimundi (despite being a carnivore it seems to be a very popular animal for children's sections of zoos)