Since you live on such a small lot, you should only consider getting hens, no roosters. Hens are not totally quiet, but you can often appease hesitant neighbors with eggs.
You can call your city zoning department and ask them if hens are allowed. Some cities out and out ban them, but others allow a small number of hens. They may have an ordinance regarding placement of a coop, however, and that could be problematic on a small lot.
If the city wont allow you to have any chickens (and
dont just take their word for it, ask them to show you the actual written ordinance) then see if you are allowed to have a few ducks. There are several breeds of ducks which are excellent layers, producing nearly as many eggs as a good hen, and they are great at eating bugs.
This is one of my Runner ducks standing next to some of my geese. Unlike other ducks, Runners stand upright like this all the time. They are great layers, too.
Welcome to BYC!
Chel