I'm a big fan of AR-15 platform, a fast handling accurized AR in .223rem is hard to beat for coyotes. I never lose the dog in the scope, so follow up shots are a piece of cake. Knocking down two coyotes with a bolt gun is a chore, not so for an AR platform. I primarily use two different uppers, an accurized 16" heavy barrel carbine for shorter, faster work, and a 24" heavy barrel rifle for longer range, stationary work. My wife shoots a .223 bolt gun (Savage 12 Varminter) for coyotes...
I've dropped coyotes with 50grn A-max's and V-max's past 600yrds with no problem.
Beyond 600-700yrds, 7mm WSM or 6.5-284. Way overkill on energy, but it takes a bit of bullet weight and velocity to get to 1000yrds accurately, regardless of what you want to kill once you get there.