RE: trapping coons
Check your regulations regarding trapping. In my state they are more or less varmits and can be trapped year around. In other states there are seasons and you need a license and need to trap during the season.
Relocating and releasing animals sounds nice and kind and all of that and disneyish. When you relocate an animal you are taking it to another area that it is unfamiliar with, where it does not know wherefood and cover are. You are introducing it to an area where there are already other animals and it is in effect invading their territory. Animals are generally not friendly to other animals hedging into thier area. If they are carrying disease, something you often won't know, you may inadvertantlyspread that disease to the new area. Relocation sounds nice, but in reality is generally a poor idea. Consider it.
If they are causing damage, trap and kill them within the bounds of the law. If you can do it in the fall and winter when the pelts have value, all the better.