While most cities don't allow small livestock farming within their limits, it's all in the definition. "Small livestock" can be pets - or at least be pets in the eyes of the city and the neighbors. That includes unusual breeds of chickens or rabbits of almost any kind.
Be sure to know your city rules thoroughly, then proceed at your own risk. If you have pets of this kind, you will have to be careful of their housing so that you are not seen as abusing them. If you have nosy neighbors, a privacy fence is a necessity.
If your pet rabbit has a litter, you will have to decide what to do with the little ones. You can raise them and take them to someone who will butcher them for you, since you probably won't be allowed to butcher them yourself in the city limits. You can sell them as pets or anything else and make a few dollars.
I have raised rabbits, but I am not an expert, so I will hand you off to this site if you decide to raise them: Naturally Feeding Rabbits This method can save you a bundle of money and make for a happy and healthy rabbitry. Nature triumphs science any day.
You probably won't be allowed roosters in the city limits, so clutches of baby chicks won't be a problem. See more about keeping chickens here: Chickens in the City
It takes common sense and courage, but you may very well be able to add an animal or two to your backyard homestead.