The problem with coons and squirrels is that they are very mischievous and when left alone, they are going to get into trouble of some kind. Maybe all animals are that way, certainly my dog is going to tear up some paper if he can find some if we leave him alone for any length of time. He just has to do something to burn off energy (or let us know he is not happy with his situation perhaps). My mother had a pet squirrel that she got as a baby. It would chew up cloths and make a bed inside of any drawer that he could get into. It got so bad, that she finally had to let it go.
I found a baby possum that I kept for a while and it would follow me everywhere I went, just like a puppy. My parents made me let it go back to the wild when it was about half grown. I never tried to domestic anything after that.
Deer must be easy to domesticate. When I was out in Wyoming, a lady there would feed a herd of deer. They were all descendants of a female that she raised and it always brought her young back to the ladies house. Anyone could feed them and they would crawl up in your lap to get some bread. One of my co-workers said that one evening she had someone knocking on her door, it was one of the deer wanting some food.
My wife said one day a little bird came pecking on our window and did this for a while. When she went out to see what was going on, she found that the bird feeder was empty. Was the bird asking for us to refill the feeder, maybe so.