ORIGINAL: HighPlainsWolfer
I'd say a 223 or 22-250. Whatever you choose DO NOT[:'(] use a polymere tipped bullet like a V-Max. They have a nasty tendency to blow up on contact at high speeds(like 204 velocity). I have personally seen 3 coyotes hop up and run off this year shot with V-max bullets out of a 204. Another was shot with a 55 gr V-max out of a 22-250 that the entrance was the size of a baseball. This one was right behind the shoulder at 80 yards. I personally use a 220 Swift with either 52gr BTHP of 55gr SP.
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I use V-Max bullets all the time and have never had a problem getting clean kills or abnormal exit holes. A shot anywhere on the head, chest, and even a couple near the stomach have resulted in clean kills. It's all about using enough bullet to get the job done. I think you are handicapping yourself with a small caliber, such as a .204.
I have had afew bullets expand before hitting the target, but about all they will do then is knock some hair off. This only happens when I hit a broomweed or something else before hitting the coyote. Part of your problem may be your barrel twist with a 220 or 22-250. A high twist barrel and high velocities don't mix well with thin-jacketed varmint bullets. The polymer tip isn't the cause, it's the jacket.