Mosey,
Why does it need to be an outside pet? Why not get them a rat and build a nice pen/cage for it in your basement? Seriously, they are supposed to be pretty intelligent and make good pets, they don't generally have a long lifespan, so when your kids are a few years older and ready for something that takes a bit more commitment, chances are the rat won't be around anymore. I have to agree with the replies you've been getting. I'm not a PETA person, but definitely don't consider pets as throwaway items because they cause a little inconvenience. Without going into your profile, if you live where it's cold, you're going to have a problem with keeping water unfrozen in the winter and that can become a big hassle as well. Even for a rabbit. I was serious about the rat, you can do more with them than a rabbit anyway.