I have whacked a truckload of 'yotes over the years, and I believe that your bullet choice can make a lot of difference regarding hide damage.
The vast majority of 'yotes I have taken were with the 220 Swift. Initially I found that hide damage was unacceptable with any bullet over 50 grains, with one exception.
It gives up a bit of BC, but the Speer 52 grain HP, with the larger open nose did not exit coyotes 90% of the time. Started at right around 4000 fps, they made a pinhole in and then disintegrated.
Needless to say, the coyotes died pretty quickly. I now shoot the 40 grain Ballistic Tip at around 4150, with similar results.
I would think that the 22-250, only giving up 150-200 fps to the Swift should be fine as well. FMJ bullets are not legal is some jurisdictions, and they do often tumble, causing serious damage to pelts as well.
My experience with the 243, 6mm Remington and 25-06 has all been: Great killing power, but substantial damage to pelts..
A shot at a coyote standing face on or facing away can allow the bullet to stay in, but other presentations....not so good.
After all is said and done, the 222/223 chamberings will do 95% of your coyote harvesting with minimum fuss and bother.
I have no personal experience with the 204, so cannot comment.
Regards, Dave.