For her 7th birthday, my daughter really, REALLY wanted a pet. We already have two dogs and an old cat so I didn't want to add any more of the larger, four-footed variety of pet. We discussed Guinea pigs, hamsters, rats, geckos, frogs and more. She wanted a pet who would interact with her and that she could play with. After lots of library books and many questions to Travis at the local Petco, we settled on rats. We adopted two who were already a year old. Meet Messi & Kiwi. They are brothers and VERY sweet. They LOVE, LOVE, LOVE walnuts and playing with the kids.
Rats get a bad wrap because of their wild relatives, but pet rats have been domesticated for so long, they are really almost a whole different animal (though they are still the same species as the wild brown rat, Rattus norvegicus). They are very dedicated and trusting of their humans.. trusting to the point that having a pet rat involves a higher stewardship to their safety. They trust us implicitly and will eat anything we offer them. Another example with our two is that they have no fear of our dogs... though they really should fear our standard poodle. We just lock her out of the room or the house when they are out.
If you are considering a pet for your child, look into rats. They are very sweet, can learn tricks and are easy to care for.