Any .22 caliber centerfire would be great choice for yotes, if your state allows it. I have a .223 and use it on them all the time. Using varmint bullets, usually there will only be an entrance wound with no visible exit wound. Other .22 calibers that would work are the .222, .22-250, and the 220 Swift. The .222 packs a little less powder than the .223. The .22-250 and the 220 Swift pack a lot more powder, and they tend to do a little more damage to the hides on close shots.

A shotgun or probably even a .22 mag would work at close distances like you mentioned.