Get some of the .22 shells with the hummingbird on the end of them. They barely make a noise. They fire from the primer alone with no powder. Alot of coonhunters use them and I assure you they will kill a coon so a rabbit would be no problem.
I know these aren't recommended for Rifles, but a lot of people use them anyway. I haven't tried them, but they seem fun. A friend of mine uses them in his carbine and just manually cycles the rounds. -bolt action would be better.