We hunt coyotes all the time and love it. You can hunt an area enough it drives them out for a while but they will be back again since there are so many and they have litters every spring just like pet dogs. there normal range is about 25 square miles.
We mostly use 22cal. center fire rifles like the 220 Swift, 22-250, 222 and 223's. We hunt when it is windy also and switch to 6 MM to 25 cal center fires. We do use shot guns in tight areas usually 12ga. loaded with # 4 buck.
We have all made our own E callers we hook to a MP3 player loaded with sounds from Varmint Al's web sight or wind rivers site.
You can sell whole frozen animals if you don't want to skin them by searching for the right buyer. You will get about 25% of fur market price for them.
Not any harder than a deer to skin. Buyers will discount a hide if it has to big of holes in it. You need to learn how to sew and also where to shot them and not blow the bullet up on a bone.
This is my home made E caller I have just a tad less than 50.00 invested in it. Uses all Radio shack parts except the cup and the specker.

Al