As a one-time keen shooter, I would tend to go for something like a 222 Remington, 223 Rem , 5.56x50 RWS or even bigger - 22/250? The main reason is there is virtually no chance of ricochet - as soon as the bullet hits something it breaks up - so does the bunny if its in the way. Not much good eating for people but the cats & dogs like them. And the noise may convince the neighbours to do their bit to reduce the numbers over the fence.
A .22 or .22 Magnum rimfire can ricochet a fair way with bad luck - even a shotgun may break a window or two.
And I've brought in rabbits by the hundred with .22's, 222's, 32/20( shot the ears off!) - only ever got 'close' with a shotgun.