Unless you have a REALLY, REALLY, REALLY good reason for wanting a coyote skin tanned, I would not suggest even attempting it. Go to a tannery somewhere and see if you can breathe. Tanning is a VERY smelly process, and if you don't live in a pretty rural area, it will run you out of house and home before you get through.
My suggestion, just hang it on the fence posts like everybody else.