Is there any reason in particular that you're looking at something larger than a .223? Longer range, heavier bullet, flatter trajectory, etc.?
Personally, I prefer a .204 or 22.250 because of the speed and flat trajectory. Only issue I have with the .204 is the small bullets don't do very well in the wind. Bumping up to a .243 would be a good option. You will lose quite a bit of speed, but the larger bullets will be able to buck the wind a little better.
All in all, my vote stays with the .204, with a 40grn bullet (take your pick on brand).
I shoot a .243 with 58 grain Vmax, I don't think you have to give up any speed. I'm not. I also use a few different 5.56's/.223, one that'll shoot well out past 500. I like my AR's for prairie dogs, don't particularly care to use them for coyotes, much prefer a bolt action; I have a .204 I use occasionally, it's great out to 400 if there's not much wind; they all get the job done if I'm shooting well. I think the .243 is the best choice if you're looking at shooting regularly past 4-600 yards (or anything less). FWIW, my .204 shoots the 32 and 40gr real well, the 45 grain sucks for keeping groups tight.

