I would think that whatever you can hit a coyote with at 400-700yrds with would be the best.
Most major popular calibers won't tear up hides at that range. I would bet that a 308 wouldn't tear up a hide at those ranges..
Use a 243 on a coyote under 100yrds and that is a lot different conversation.
I guess my point is, if you go into a bigger sports store and look at the shelves, (some of them) have at least 1/3rd of their choices as something that would work for Coyotes. There are a pile of choices, and almost everyone here will give you a different answer. I don't think you could get them to all agree on a single weight bullet in a fixed caliber, and it's all over if you ask about manufacture.
The challenges you are facing is getting a bullet that is going to give you sub MOA accuracy, something that will carry the energy needed, or deliver all it's got on impact, and something that isn't going to rip up hides.
That's tough, since to get it out there, it has to be moving, so that means that your tearing up any close up shots of under 100yrds. That also means that you have to think about the type of bullet you want. I like Vmax or simular bullets, others don't. If i shoot a coyote at 500yrds, I want him to drop dead.. Right there.. Called DRT. I don't want to walk out 500yrds and then search all over for a coyote too, that ran off and died somewhere. I can promise you that if a coyote runs on you, and you don't see it drop or roll, it's gonna die under a bush or in a hole or something that makes it a pain to find.
I like a fast caliber, flat shooter, and carry a shotgun too. I can reach out as far as i feel comfortable, and at under 300yrds i don't have enough drop to need to really adjust my hold over. 500yrds is about 15" of hold over. THe shotgun has BB 3" shells and handles anything inside of 50yrds.
Good luck.