Buy a box of Remington Core Lokt 55 grain soft points (or Hollow points if no soft points available) and try them for accuracy in your gun. You can usually find them on sale or with a rebate available and they may just shoot for you, they would work fine for coyotes at 150-200 yards. I have a Handi .223 that will put 3 of those in a group you can cover with a dime at 100 yards...<><....

Also there is a lot more to shells and bullets than diameter, for one thing military ammo, designated as 5.56 is usually loaded to "hotter" or more powerful loadings than commercial ammo, many of it is loaded in steel cases, some with a laquer or painted exterior, all of some of these changes can lead to problems, not the least of which is empty shells sticking in the chamber of your .223 Handi, just don't do it for now on these suggestions, you will soon learn more and things will become clearer....<><....