Having hunted 'yotes for 40+ years & having developed a world of respect for their intelligence, endurance, & tenacity, I have to sound an emphatic NO WAY on both .22LR AND .17HMR. Unless they are point-blank & you can hit them in the head, these calibers are NOT appropriate, period! I'm sure dogs have been successfully & quickly dispatched with said rounds, but more have run away to die a lingering death. A 12 gauge with buckshot will be effective at 30 yards or less, but a good centerfire handgun or rifle is the best tool . . . .17 Remington (200 yard gun), .204 Ruger, .223 . If I'm anticipating long shots, I use a .243 or .25-06. Be responsible & fair to your quarry. Coyotes are TOUGH!