You didn't mention that you're after fur so I'll assume you're out to lessen coyote depredation on game type critters.
When it's really windy, say over 20 mph, in my book the 7 Mag w/ the 162 Amax can't be beat.
Winds of 10 to 20; the .243 w/ an 80 grain or the .308 w/ the 155 Amax are good to 500. Heavier is better in the .243 if your rifle shoots them; mine like the 100 grain Remington bulk bullets, I like the price.
Less than 10 mph, and ranges expected to be less than 250, the .223 and 50 gr SPs. Have tried the 68 and 75 grain .224s in the .223 w/ 1 in 9" twist, but with hits at 400 yards plus, it's been my experience that too many run off. Fox, okay; coyotes, no.
For me, the .223 works fine in the early part of the season; as they wise up, the .223 just doesn't cut it. My wife calls them in close, and loves her M70 Fwt in .223. We do the "drop and drive" a lot; I get the long shots, she gets them up close.
Without more info, my advice would be to go with your 7 Mag and the 162 Amax. You'd be very hard pressed to improve on it. I've not taken any past 600 w/ my Sendero yet, but have come very, very close. And close on a suspicious, walking, 900 yard coyote is quite satisfying, believe me.
Don't know why I'm weighing in on this discussion, as I'm new here, and no expert. This is quite a forum; I've learned a lot just nosin' around the last year or so. Thanks!