Leader Drop Traps are what you want.
http://www.rabbittrap.co.uk/
You dig them in permanently to a
fence line and they have a tunnel through the
fence. Over time the rabbits get used to using the tunnel so then you remove the lock from the trap. When they walk through the tunnel the floor drops away beneath them and they end up trapped in a subteranean box, while the trap is counterweighted to reset itself.
In the morning you come around and dispatch the rabbits and lock the trap. No chance of accidentally killing anything you don't want and they remain effective for years. They also remain effective with low rabbit populations, where most other methods become progressively more expensive and difficult (it is easy to get someone to come and shoot 50 rabbits when you have a plague, a lot harder when you have just two rabbits eating your lettuces!).
I've thought for a while that there would be a good side business in installing and servicing these for nearby farms. Get paid an installation fee and an ongoing contract fee to set and empty them every few weeks, plus you get to keep and/or
sell lots of rabbit meat.
First few minutes is installation, the rest is using them.