I live out in the country now and can shoot any type of gun legally, but I still really like the .22 short CB's since they make no noise. They don't make any more noise than a pellet guy and they can easily kill small game. If you have a solid backstop to prevent ricochet, you could shoot those and your neighbor won't hear it.
The rabbit numbers this year are unbelievable around my house in SE MN, but that makes me very happy since I really like rabbit hunting. There are multiple age classes of rabbits running around my yard every night - it should be an excellent rabbit season this fall.