A possum made a home under the cement floor of the garage in the house next door. I told the guy how to get it to move on and it wasn't a problem. Possums move/change homes a lot anyway. They eat ticks....are almost immune to rabies, venom from snakes and many poisons. They clean up carrion, garbage with their 50 sharp teeth.
We have a ravine a block down the street so the skunks and raccoons seem to prefer to live there. The raccoons that come to my yard have been trained not to touch the sliding glass door or the screen....it's so funny watching them try to stand on their hind legs without leaning on the door or the screen!
Regarding coyotes...I don't think I would lure them close to the house or try to tame them.