Quoted:
It's a coyote, anything out of an AR will work. Hit it in the vitals and done. It's not an elk at 500 yards... Don't over think it. If anything you need to look up SC game and fish laws and make sure certain ammo isn't banned or mag capacity isn't limited. Other wise get some calls, camo up, and be patient and be ready to learn.
This is what I came here to say. The only thing I would add is that your current setup is fine, start with that and adapt as needed. And use a good hunting round - I prefer the VMAX in the 55gr or 62gr variety, mostly because they are cost effective, have good terminal performance, and are readily available. Another round that I have used which has worked very well is the 69gr Sierra Matchking. The Barnes bullets are a darn good choice, as well.