For coyotes, a .22-250, .223, .220swift, and .204 Ruger will all offer pretty similar performace on coyotes (or .222 rem, or .222rem mag, among others). They're all going to do the job out to 600-700yrds if you can place the bullet well. The .204 Ruger generally runs lighter bullets than the other 3, but still offers great down range performance on coyotes.
My personal choice is the .223rem. Then again, I'm a fanatic for the AR-15 platform. I ran a .22-250 for coyotes for 10yrs, then gave up the .22-250 when I transitioned over to AR's, and haven't looked back.
The major advantage of the .223rem is that it's the lowest pressure of the lot, and therefore the nicest on barrels. If it's JUST a coyote rifle, you'll never notice the difference, but if you run it over a bench much, or do much prairie dog hunting with it, you can easily burn up a barrel with a .22-250 or .220swift (making the same bet for .204 Ruger and .223WSSM).