That Remington SPS Tactical in a .223 would be an awesome Rifle with plenty of knock-down power for Coyotes....and those grains of bullets are going to be fine and will carry out well and still have plenty of power to drop Coyotes,Bobcats or Foxes.
I'm shooting a CZ-USA .204 "Varmint" with the heavy barrel using 32 grain Winchester ballistic tips and have also used the Hornady V-max 40 grain bullets and will switch over to the Federal loaded V-Shok Sierra Blitz Kings in 39 grain pills!
My Coyote Calling Partner has used His .22 Hornet and .22 magnum for shooting Coyotes and they are smaller/lighter grain bullets than most of the .223.