Have you considered adopting??
http://www.petfinder.com/
This is an amazing national site and they have alot of very sweet animals looking for homes, mostly due to owners no longer being able to afford keeping them.
I would suggest a rabit. Specifically a "mini-lop"
http://animal-world.com/encyclo/crit...ts/minilop.php
They are big enough for a child to cuddle with, but small enough to contain. I had one when i was younger and i adored him, he was one of my best little pets ever.
Good luck in finding your new furry family member!
Sweetpea