Soft wad cutters are probably your best bet. You're going to watn to have very, very good accuracy, too.
Also, and most importantly, you're going to need to know what you're shooting. If they're song birds, you stand to have some trouble. However, since you're in the city, I'll just bet it's starlings. That or house sparrows.
Actually, in the city, you stand to have trouble regardless, but you at least have most of our moral support on this matter.