Not sure about the fur part. I'm in NH there's some nice fur on some. But the last few have had some mange. I love hunting coyote I use all 22 caliber stuff. 22 hornet, 223, 225, 22-250.I load them all with light v-max bullets and hollow points. I very rarely have a hole or a pass through. I think the 223 is a hard round to beat for coyote and have taken most of mine with one. It causes little damage on the outside but wrecks there insides. The 22 hornet is kinda light I've found if your past 100 yards. On the ten I've shot since February only two were messed up and they were shot with the 22-250 with 55 grain soft points.
I've heard the 204 ruger is awesome on coyotes and am looking into getting a barrel for my contender. I'd imagine it'd make pinholes on the way in and just fragment once through the skin.
I bait and call them and would say my average shot is 150 yards. But I've shot em as close as 25/30 yards and as far as 300+ yards. But most common just over 100 to 150 yards. My only reason to get rid of em is cause there's tons too many. And not so many rabbits and partridge and Turkey as there used to be. Plus its tons of fun!
Good luck and kill em all.