Hmm, a suppressor that is illegal in virtually every state for hunting and does nothing for the supersonic crack? A 17, 204 or 224 suggested for long range where wind is going to be more of a factor?

Your 308 is fine with deer bullets. You will have 30 cal holes to sew up if you save hides. Don't buy into all of the hype that you need this or that. Just set up with the wind in your face. Use a feather on a string dangling in the wind off a sapling. Or a weasel ball flopping around in the field. Obstruct yourself with cover. Learn to call off of open and closed reeds as well as a caller if you use one. Also have some sort of a coaxer like a mouse squeak. Start out calling low in case some are nearer, as you don't want to blast their ears out. Increase the volume over time. 15-20 minutes should be about max for a stand. Kill the calling for the last few minutes and sit tight seeing if a weary one is eyeing your stand. Move to another some distance away and start fresh. Watch the birds, if they get spooked up then odds are something made them that way and is headed your way.
As for caliber, just use what you have. I've done it since a child. I have several 17s and 223s. Personally these days I use a 40 cal muzzle loader. I have used about everything over the years. Coyotes are easy to kill, you don't need a super bullet. Permanent wound cavities do them in with a center fire not intended to be frangible. If later on you want to go to a varmint caliber that is fine. But the only few disadvantages a deer bullet has is the two holes, more likely to ricochet and the cost per round. A fella can sew the holes and not get docked by the furrier. It would take hundreds of coyote to offset the price of a rifle. The main factor is the ricochet so just be careful where you are shooting.