Animals and Pets

I worry that whatever you choose, your son will be dissatisfied. Maybe your kid is different, but most the kids I've known wanted a pet they could bond with. They've wanted a pet that was interested in what the kid does, that silently listened to the kid expressing their issues, and that offered things to do, like: "feed me", "pet me", or "play!"

Rabbits might work, but they might be too interested in one another. Even if they weren't forbidden, you'd run into the same issue with social birds like cockatiels. The only pets I can think of that give kids the attention a kid craves are the animals that have lived with humans for hundred if not thousands of years. Basically: dogs and cats. After that you get into cows, pigs, chickens, goats, and the like. Goats are wicked smart, but the males stink to high heaven unless neutered young. If you raise geese from goslings, they will love you forever and ask for cuddles whenever they see you -- but they have to stay outside and do make a mess. Someone else might correct me, but I doubt you want a pig -- partially just because they end up getting so big (I'm told there's no such thing as a teacup pig).

If the only issue with dogs is allergies, you could consider a low-allergenic breed. Dogs are simply the ideal pet for people with the time and space for them. They've lived with humans nearly forever and do all the stuff a young boy wants from a pet. Cats require less attention and can be caring and affectionate if they want to, but that depends on the particular cat. I've had turtles, ferrets, parrots, fish, and lots of other animals as pets and only the parrots and ferrets held a candle to dogs and cats. Fish-wise, I found the most exciting to be South American Cichlids -- but mostly because I had a Green Terror who fell in love with a Blue Acara overnight such that the two of them tried to kill everything in the tank in the span of 10 hours. I got them their own tank where they raised many babies.