17 HMR is a 22 magnum case necked down to .172' diameter and the 17M2 is a 22 long fifle case necked downt to 172' . with a 17 grain bullet the 17 M2 give about 2100 fps from a rifle and the 17 HMR delivers about 2600 fps from a rifle also. Im not sure about the size of the coyotes in your area but the 17 HMR is completly capable of taking a coyote under 100 yards. Im talking from personal experience here too. i would be kinda shy about using the 17 M2 on coyote though. as for using a 22LR on a coyote, if thats the gun you can shoot, use it. a chest shot will work but should be avoided at almost any cost as the animal would run a great distance. Just make sure that you use a good scope that is zeroed correctly and dont shoot beyond the distance that your gun can keep 5 shots under an inch and a half. follow these directions and you should be fine.

you really shouldnnt have to do any thing to an AR-15 except mount a scope for coyote hunting.