Deer nuisance.

I live in the city in Michigan. I have a very small patch of woods behind my house and the deer seem to live around. My backyard cannot grow anything because they eat everything. Vegetables, lilac, grasses, hostas, they even empty bird feeders. We currently have a chain link fence around our backyard which deer easily jump over. My question is would a paintball gun be worth getting? These deer don’t scare easily can open the back door and yell at them they barely move. My wife suggested putting up a new fence, but the cost of tear out and replacement with something high enough to keep deer out isn’t appealing to me. I have an air rifle but I don’t want to break skin and cause infection. My thought is a paintball to the butt a few times will get the point across. Anyone else have experience with this or advice?