RE: deer hunting
Yes, a 7mm Rem Mag will kill a coyote very, very dead. If you don't care about the hide, then by all means blast the little SOB's to kingdom come with your 7mm. Coyote are vermin in most parts of the country. Around here the coyote will kill deer (mostly fawns), turkey, pheasant and even will maul newborn calves. I've seen pictures of calves partially eaten alive. Needless to say that the farmers don't want them around, and will nail them themselves if they get the chance.
Now, if you do want to sell the hide, the 7mm Mag isn't the best choice because it's going to seriously mess up a 40lb coyote. You might get away with using a solid or FMJ bullet, just beware of ricochet.
Mike