Stihl27: I have shot, and kill't, 3 Coyotes with my 17 HMR Rifles since 2,003 - all were one shot kills and all were pretty humane kills.
I, of course, would choose other cartridges as my first choice when going on a dedicated Coyote Hunt but when thats all you have along and the range is conducive and shot placement is careful - it WILL kill Coyotes.
Keep after'em!
Hold into the wind
VarmintGuy
