Well maybe not THE definitive answer, but it does reflect my opinion. :grin: The .22 Hornet will accomplish your tasks quite nicely. In fact, I would not hesitate to use a 10" Hornet on a coyote out to 125-150yds which I would consider maximum range for bigger varmints.
So for your requirements, again I say that the Hornet would be perfect. However, if you wanted to push the performance envelope in a 10" gun then I would lean towards a .221 fireball. The .222 has a bit too much case capacity to make it a nice round for the shorter barrel.
I've played with the Hornet a fair amount now. You can expect up to 2600fps with bullets in the 30-35gr range, but I really suggest that you take it easy on the brass because it can have a tendency to be pretty thin. So keep your loads <90-95% of max and it will serve you well and you'll love it.