haha what? geez, 7mm rem mag?

I think .22-250 .220 swift, at those distances I'd say the .220 would be a clear winner out of any .223.

Or a .243 / 6mm with 55gr, or 25.06 with light bullets, though .257 wby with 87gr woudl be awesome I think at 500-700 yds if not further.....I think 7mm 168gr is a tad huge!

.270 w/100gr might be awesome, or even 130gr.

both of the .22's mentioned will do 500yds no prob on a coyote.