I also have a 22lr that I can hit a can at 100 yards no problem but 9 out of 10 coyotes you hit will probably run to the county. Even head shots are a big problem with something that small for alot of shots. A 223 I'n my opinion is best for coyotes and then use Full metal jackets and small hole I'n and small hole out and coyote hits ground and stays there and you can even make shots to 250 yards easy! Plus the ammo is about as cheap as they come and if you're a reloader it's even cheaper. 223 Best coyote medicine hands down. Yep go price ammo for a 22-250, 17, 204, or whatever it's pricey and basically a small bullet. And for your 30-06 you'd do too much damage to pelt and again, check price of ammo.
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