If you dont want to kill them id try live traps. Just be sure to let them loose far away. Killing is the fastest way but not everyone wants that responsibility and i completely understand. 

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I do not think they deserve to be killed- that is a very horrible way to get rid of them and it could also attract predators which is worse than having a bunch of rabbits.
How many are you talking about? A family could be 20 or more. Trapping them all would be challenging at best. Dispatching is a viable option. There are humane methods. I have personally not had any results with moth balls. I did have marginal results with fox urine. I don't envy your position, but if left unchecked damage to the shed and yard is inevitable. Also as others have said, predators will start prowling. I don't know if you have any children or other pets but having things hunting your yard is rarely good. Best of luck
I do not think they deserve to be killed- that is a very horrible way to get rid of them and it could also attract predators which is worse than having a bunch of rabbits.
Have you got a cat? Some well-placed ... ummm ... clumps .... have been effective for me. I strategically put them around and just inside the tunnel entrances. The rabbits got the idea that there were predators lurking about and moved on.
.... Killing is the fastest way but not everyone wants that responsibility and i completely understand.
If a good shot, they won't even know what hit them.I do not think they deserve to be killed- that is a very horrible way to get rid of them and it could also attract predators which is worse than having a bunch of rabbits.