I bought a .22 Webley FX2000 when they came out, specifically to control the Rabbit population on some land belonging to a friend.
I successfully accounted for quite a few, but have to admit to being a bit put off by watching the flight curve of the .22 pellet, so bought a .177 FX 2000 as soon as they became available, and accounted for even more rabbits without the annoyance of watching the flight curve of the pellet, so yes, .177 is fine for Rabbits as long as your accuracy matches the performance of your rifle.