For fur handling tips here's what I suggest:
On shot coyotes or trapped coyotes, pull the hides as soon as they're shot. It may cost you a little time ( over the course of one day of calling it might cost you one stand) but it gets the hide cooling A.S.A.P. and prevents the hide from spoiling and stops the hair from slipping (falling out). I know this drives my hunting partners nuts (Dogleg can attest to that

), but it will pay off in the long run.
If you can't pull the hide right away , hang them by their back feet in as cold a place as possible. This will drop their guts into their chest cavity and prevent what's called "green belly".
Don't waste your money on a "skinning knife". Buy a cheap paring knife and use that as your general purpose knife. They're cheap, hold a good edge, and light weight.
If you can find an old wringer washer , use it to wash your hides. The reason for the wringer washer is that you can run water into it as it's being pumped out. The water may start out dirty and bloody but it eventually clears up and then you know you have an absolutley clean pelt.
There's a bunch of other stuff I just can't think of right now. Just always remember to take your time and have fun. Putting up fur doesn't have to be a chore.