Since we are not after fur, and are just trying to save our deer population, I use a .30-06 loaded with 110 gr Hornady V-Max with 54.9 gr of H4895. Have not lost a single one. You might not find all the pieces though. Devastating. I definitely do not take the kids with me for coyote hunting. Too gruesome for young eyes.
I picked up a Model 100 in 284 Winchester, I ordered a set of dies this AM, I have 120 grain Nosler Ballistic Tips, and Hornady 120 grain Vmax on the desk as I type. I'll use which ever one shoots best, but no, I have no interest in pelts.
You should find a fur harvester/ hunter to take with you. No sense in wasting a good pelt? I shoot 55gr. sierra's in 223, and 70 gr. Nosler B.T. in 243 on a windy day, but both are pelt friendly, and still crush them as dead as a 300 win. mag. Close ups a M.B. 835 12 gauge with a Carlson choke tube and some 0000 buck kills them pretty dead too. I save the blowing up of pelts for my Wood Chucks and 243 cranium shots.
Michiganhunter, even the trappers in this area aren't bothering with coyotes. Too much work for the prices they are fetching. Two years ago prime coyotes were only fetching $8. Last year they went down to $5. Most fur buyers are even refusing to buy them as they are not making enough profit off them. And since they quit trapping them around here, their population has boomed. So us deer hunters are trying to keep them in check. That is why I am using my .30-06.