Where I hunt I have to use a shotgun. My favorite rabbit gun is a single shot 20 guage and it's been my rabbit gun for years. I use 8 shot instead of 6 most of the time and it works great. Rabbit's are pretty fragile and just the shock of getting hit by the pellets, regardless of whether they get in very deep will kill them almost immediately most in most cases. Any lead pellets in the meat can be easily seen after skinning and removed. If you happen to get one in a bite of something, the soft lead is easier on the teeth than steel, as someone pointed out earlier.
"I prefer dangerous freedom over peaceful slavery."
- Thomas Jefferson