A live trap baited with marshmallows or sliced apples works great. You don't catch the family cat (or the neighbor's cat) that way. Once, I caught 5 in about a week and a half. That seemed to clear out the group that had us targeted.
What appears to happen, sometimes anyway, (just making guesses based on what I've seen here) is that a gang of coons, probably a family, mom and babies, will find your free lunch counter. Then they'll keep coming back until all the birds are gone, or you stop them.
Once you capture or kill that group, usually things will be ok, at least for awhile. There are lots of raccoons around us, we're out in the sticks. But I've only had raccoon trouble twice, in about 12 years. Once was last year, when I caught the 5, the other was when we first moved here, we trapped 2 and shot 3. Oh, one other time, a single raccoon was stealing the food from our outdoor cats, one of he dogs treed him, my DH shot him. That one went in the crock pot, after I brined hm for a week in the fridge, really tasty!
Where I am, I can do whatever I want with them, and FYI, raccoon is delicious.
If you are in an area where you can't shoot them, or otherwise dispose of them, you can call either Fish and Game, or Animal Control, and most places they'll come and get them. Then it's their problem. Even out here, the game warden will come pick up a coon or other varmint if you call them. 
There is an area no too far from us, about 20 miles, where there are no humans habitations anywhere close, there's a river, and a lot of woods. Plenty of wild food sources, and easy access to water. I have released raccoons there, if I didn't have time to butcher them. I would NEVER release them where they would be likely to become a problem for others. I just don't like to kill something I'm not going to eat, unless I really have to. Wild animals have no concept of ownership, they just find food, and take it. They aren't evil, they aren't out to get you. They're just surviving. I don't try to "get even" or try to punish them. There's no point. I just do what's needed to protect my poultry, pets, home, and garden.