For a small projectile, high velocity load like a 5.56mm, what would be the optimal cartridge to use on thin skinned game such as deer, or coyotes? I'm talking about which load has the best wound channel, and does the most damage, along with is economical and accurate.

I use the Winchester .223 Hollow point varmit rounds that boast 3600 fps that come in a box of 40 and are pretty cheap at Wallmart. They really will mess a coyote up if you hit him at the wrong angle but I have not yet had a coyote run after I have hit him with one and it only takes ONE to kill it instantly.
They are a good price and they are very accurate to and I love them for hunting and sometimes plinking but I usually buy the cheaper stuff in bulk to plink with. Hope that helps you.