RE: 243 for bear
I wouldn't suggest it but if that's your only option then you could at least try it, it will definitly have to be a well placed shot. Also, I don't hunt coyotes but I do often see many "varmint" rifles chambered for it, you can buy buy 80 grain factory ammo and if you handload you can get even smaller bullets or FMJ bullets so there's no reason not to use it for coyotes