Good pets for people with asthma and allergies?

I've been thinking of getting a pet, but my dad is elderly, has asthma and is allergic to cats. Not sure about dogs, but given his age, I don't want to take the risk.

I'm looking for a pet that is affectionate and can bond with humans, so preferably no reptiles, fishes, or insects.

Would birds trigger my dad's asthma and allergies? Or does anyone have any recommendations?

We live in a tropical climate. It's very hot and humid all year round, if that matters.