A small connibear placed in a rabbit run will produce the a quick, clean kill. It will also kill anything else that comes down that trail as well.

Conbear traps are expensive and if something big like a deer steps in it, he'll probably walk off with it. Snare wire costs pennies.

check with your local d.n.r snares are illegal in many places . have you ever tried a dead fall with a figure 4 trigger . its better for squirrel's but it may get you a rabbit as well if made big enough . look on line for a diagram of how to make the trigger its not that hard to do but but it is a bit hard to explain in print.

i also think a split log dead fall will work it takes a little more force some times but it wroks well