I'd use a 22-250 if necessary - but I prefer a .243 or .257, personally.
When buying my last coyote rifle that would also be used for deer and wolves, I chose a .25/06 because the store couldn't get me that rifle in 7mm/08. I turned down the CF .22's and the .243 - both available but any would have worked just fine. Whatever you have confidence in.
-------------------- Daryl
"a gun without hammers is like a Spaniel without ears" King George V