The 223 is rather effective on Deer with a proper bullet.FWIW - None of the three cartridges you listed are "good" deer hunting rounds. They can be used, in some places, though most states ban them for hunting deer...and with good reason.
This thread is about nothing but Deer taken with the 223:
Shot location is the most important and then the bullet.
I'd bet that a properly place 45 ACP bullet will most certainly stop a Couger pronto