Use whatever shoots best from your rifle. No bad choices, other than the size of the hole they'll leave. The .243 will anchor coyotes without issue, no matter the bullet used.
and all bullets from this cartridge, if loaded to "normal" velocities, are going to leave an exit hole on a broadside shot. Loads using powders such as Trailboss do not quality in this statement.
I've used 55 & 70 gr Nosler BT's, Sierra SPBT's of various weight, and various Speer bullets as well. Since I use 100 gr bullets for big game with the .243, that's what I've shot a majority of coyotes with, too.
Right now, I load Speer 100 gr SPBT's almost exclusively in this cartridge. They shoot extremely well from my rifle, and cause far less damage to meat than Sierra bullets I've tried, with better penetration. I refuse to pay extra for Nosler Partitions or Speer Grand Slams in this cartridge, mostly because they have a lower BC, and I've seen no real improvement in performance on game from them.
If the furs are to be saved, I highly recommend something like a .223 or .17 Remington. The larger centerfires are hard on coyote fur.
Daryl