I’ve never shot 77SMK but I’ve shot a bunch of coyotes with a 223. I’d recommend 50 or 55BT or 55vmax. I’m sure the 77SMK will kill them if you hit them properly but I would much prefer the faster, lighter bullet for the ranges you are talking about shooting. As others have mentioned, your 243 is an extremely effective coyote round. Load it with 55BT and it will turn a yoties lights out instantly. I wouldn’t worry about the glossy finish of your 243. I’ve never met a coyote that knew what a rifle looks like. They’ll see your movements whether its gloss or not.