I've never sold coyotes hides...but I paid for my first vehicle (1973 Jeep) with fur money, mostly mink, muskrat, coon, fox, and possums (don't laugh, a big one would would bring $5 then)
All critters skin about the same...the hard parts are the tails on the ones with furry tails and the ears....I whacked the tails several times with a hammer, they pulled right through...ears, you just have to be careful and watch what you're cutting.
Stretching...I had boards cut to size for each critter, sorta shaped like a bowling pin but without the skinny neck, stretch them over that, clean them off, rub them with salt, let them dry.
Skinning...I believe there are videos on YouTube that might do a better job of explaining it.
It's good to know how to skin coyotes at home, but in the country i hunt i often have to skin in the field as i'm a walking hunter and sometimes i'm several miles from the vehicle. Just skinned one yesterday in fact off a T-post, and it took me about 20 minutes, then i was off hunting again. Once you learn to skin them according to the instructions given so far, learn to skin off a fencepost, as that may be necessary sometime.
In the past few years I have been using concave faced knives for the opening cuts. I have used the same knives for opening up moose, caribou, coyote, and muskrat.
The Outdoor Edge Swing Blade is easily the most useful and fastest skinning tool I've ever seen. Gerber also makes a concave blade skinning knife. The Kershaw Blade Trader with the great big gut hook works well. The Wyoming knife works good also. I'm going to do the air skinning method on my next animal. Between the opener knives and the air. It should be Way fast.