Is it legal to set 110s with the sole intention to catch rabbits?

Is there a rabbit trapping season?

Not listed but it also says no equipment restrictions. Darn things are digging all sorts of holes under my deck and in my yard. Live in a neighborhood so I can't shoot them.

At the point where they are causing damage, they become "nuisance wildlife". Unless there are NA restrictions, I'd say have at it! Some recent rule changes (2015) allows a landowner to take nuisance wildlife without a permit. BTW-110's do nicely on digging rabbits. Might want to be sure there are no skunks though!!!

Use a live trap and bring them rabbits to me

Havent seen a skunk yet. If any are caught they will get eaten for sure. My son wants to shoot them with his bow. No houses behind us but im not sure momma would like me waking him up at 11 or later when I see them for him to get outta bed and shoot them.

Air rifles are quiet enough and work well on small game. In case you ever want to take the more direct route. Those Greenwood coyotes might appreciate you trapping the rabbits for them.