You are much better off to shoot the coons, cats, ect than to relocate. For one is most states it is illiegal to relocate live animals two you are just giving someone else a problem. You will being the critter a greater in justice by relocating it. It will most likely be attacked by the resident criiters and may very well starve. If you are worried about being cruel to the animal then just keep feeding it your chickens.
Relocating Problem Wild Animals
Not as humane as you might think
Many people believe that it is more humane to relocate problem wildlife than to kill the offending animal. Click For Euthanasia Chambers While on its face, this idea seems to make sense. Taking the animal and putting him back into the woods, "where he belongs" sounds reasonable.
Unfortunately for the animal, relocation has a number of bad side effects.
1. Relocated animals must find new food sources in an unfamiliar environment.
2. Relocated animals must find new shelter in an unfamiliar environment. In the winter time, relocated wildlife have precious little time to find shelter.
3. Relocated animals must do number 1 and 2 above while avoiding predators. It must also do those tasks before weather, food and water conditions take their toll.
4. Your relocation may result in the deaths of young through starvation that have now lost their mother from your relocating her away from her young.
5. Relocating animals raises the risk of relocating a disease like rabies to new and uninfected locales. Like what happened with the Mid Atlantic Rabies Outbreak.
6. It may also be illegal in your state.