Are you technically not allowed to have chickens by county rules? We started off with illegal chickens as many people do. We did, however, ask our neighbors before we got any. At the time we lived in a fairly rural area/county and for some reason seemed to be the only community in the county that couldn't have chickens. None of our neighbors cared however so we went a head and got for EEs. Over all they were pretty quiet. There was one that sang loudly after laying but it didn't last too long. Honestly you couldn't really hear her if you were inside anyway. And if you went out after she laid she got pretty quiet. I will say that we thought it was really loud because we weren't supposed to hear them but none of the neighbors ever heard. And we gave away some eggs when we had extras so there were no complaints. We also disguised our coop and kept it hidden from view so you couldn't really tell where any noise was coming from.
It seems pretty hard to say certain breeds are more quiet then others as it's very individual with each chicken. Just having a few hens is a lot quieter then neighbor dogs (and I love dogs). We currently have guinea fowl as well and those things, notorious for being noisy, hardly make a peep. Every once in awhile you'll hear the machine gun sound or a quick buck-wheat buck-wheat from the females, but we've been pleasantly surprised by how quiet they can be. If you have a good relationship with your neighbors that may be your best bet.
If birds turn out to be a no go, I can say that house rabbits are a wonderful pet. You can litter train them, train them only to chew on appropriate things and they can hop around your house. The chewing is the hardest part with house rabbits though so just be prepared if you go that route.
