One of the boys on Predator Hunt Canada recently smacked one at 477 yards with his .204. Considering that and the number of coyotes he tends to collect, I'd say that's pretty good evidence of its capability.
I should add that I would not advocate the .204 for wolves.
Yup that was quite a shot by that member no doubts there.
To the OP
Any of the previously mentioned Cals from 204R to 25-06 will do their job. Each one having distinct benefits over the next or its' counter-part. I've listed the ones I use below which may-or may not help with your decision.
204 Ruger - As flat as the 22-250 , but 2-300fps faster & gives up about 2-300Ftlbs of energy over the same ranges. Alot quieter then its bigger brothers, which is nice if your working near buildings, roads or livestock. 35Gr Bergers or 39Gr Sierra BKs' seem to be the best bullet choices for hand loaders.
22-250 Rem - The "all rounder" Quick & flat shooting with a ton of bullet choices to be had. 50-55Gr loads are most commonly used. Quite possibly the most widely used Yote round until the 204 came along.
.243 Win - Ample amounts of 6mm sized bullets to choose from for loaders. Handles wind alot better then the .20 or .22Cal bullets. Easily reaches 400yrds + with a sh*t load more energy behind it. Not the most pelt friendly round by any-means, so expect fist size exit wounds. The sweet spot for most people that are using .243 is between 70-90Gr loads. Can double as a nice light duty Deer rig if called upon.
Any of the other Cals mentioned (222Rem, 223, 25-06 or 270Win) are equally capable. Throw in 6.5x55mm Swede, 260 Rem or 6.5Creedmore and you just add to the confusion

Just remember the last five will be throwing 75-140Gr pills down range. They're more Deer cartridges with the ability of being Coyote rounds if needed. As always, ymmv
Best advice I can give is pick a .22Cal cartridge and get out calling/hunting. Put a season or two under your belt, then you can decide if you need to move up/down or add another 'Yote rig based on your actual stand scenarios
