I kill over a hundred coyotes a year as well as guiding, so I skin a lot for clients as well. I do them in the field when they are still hot. It takes 7-8 minutes to case skin for fur market. It only takes newbies about 15 minutes. If you want to mount or have the paws attached, it does take longer and I do that at home.
With the coyote on the ground on his back{preferably dead}, I cut from one hind foot to the other on the dotted line between the fur on the outside and the fur on the underside of the coyote. I use a fixed blade with a gut hook and use the guthook for this cut.You can use any lockblade or fixed blade.
Next I cut the hide around the front legs, above the elbow. I don't worry about cutting flesh or tendons.
Take a piece of parachute cord about 18 inches long, with a loop in each end and attach a loop to each hind leg between the toes and the hock.
Hang the coyote/fox on a fence post so he is facing the post, with the tail facing you. I use the gut hook again and split the underside of the tail to about 3-4 inches from the end. Take your time here, there are other places to go fast. Once I have the tail split on the underside, I cut on either side of the anus through to my previous leg cuts. I don't worry about cutting muscle or tissue. I take care not to cut the Achilles tendon, as it makes skinning more difficult.
Now I work the hide away from the ankles with my fingers and cut a ring around to free the hide.With only my hands, I work/pull the hide down over the hips. I then work the tail free of the split hide, and strip the tail out. Some guys use a tail stripper, 2 screw drivers etc. I just use my hand, and pull grasp the tail and pull down, letting the tailbone slide out of the hide.
Now things get going a lot faster. The hide will take a lot of pulling without tearing EXCEPT bullet holes and rips, which tear very easily.I pull {hard} the hide off the body and over the shoulders.
I can now turn the little bugger over and push the fur away from his elbows with my fingers. I work the leg out of the hole and when I have both front legs free, I use those holes as new grips.
I pull the hide over the head and as the ears are exposed, I cut the cartilage off flush with the skull. I now have two new hand holds. I stick my fingers in the ears and pull. As the hide comes over the eyes, I carefully cut the eyelid to stay with the hide. I then cut the lips on each side allowing me two more new hand holds. Pull and trim the lips away from the jaw and cut the nose off to spite his face.
You're done and it took way longer to type this than it does to skin one.
The hide is then fleshed and stretched, ready to be sold or tanned.
If you want feet/toes, then it takes longer and I do that at home. It takes me about 1/2 hour.
Try
www.predatormasters.com They have a trapping forum with tons of tanning info.