Billy, What you say may be quite true about the .204. One of the top coyote hunters in this area had one on a hunt where I went along. He used it on one coyote that day, I got one with the .22-250 AI. I am not sure what load he had, but the AI kicked along a 50 grain Blitzking close to 4000 I believe. I would have to look back at the notes. The dog I killed was a bit farther, the the destruction a good bit more. For my use at age 62, I don't want to stock up on 20 cal. bullets, cleaning rods, patches, etc. for a caliber that I feel I can equal or better with a hot .22: AI, Swift, or Cheetah. While you may be right about the higher BC, I haven't checked, but I learned about 25 years ago, when there is wind, the .22's are best left in the pickup, and a heavier rifle taken.
Now this does not apply to all coyote hunting. Certainly not the east, midwest, and much of the west. I have come to realize, this area provides an unusually high percent of shots at coyotes going about their daily lives.
I have not run into an area like this anywhere except near Albany, Tx. They didn't shoot at coyotes very much on that ranch.
For calling I think the .17, 204, .223 or big 22's would all be fine as shots are usually fairly close.
I am sure it seems strange to many to have a .300 for coyotes, but my pal and I use bigger rifles from Sept. though the spring hunt. He usually has a 26 inch barreled 6mm, and a 27 in. barreled 7mm Mag. in the truck for spot and stalk hunting. I usually use a .25-06, and my heavy .300. When I hunt near ranches, or a lot of stock, I take the Swift, .22-250 or AI. But here ranges will be short, due to the stock in the fields. I have come to find this coyote hunting we enjoy is rather unique in the coyote hunting world.