The 25-06 will most likely have pelt damage no matter which round you use, BUT it will do the job, so use it!! As far as calls go, every call that is on the market will work, in the right hands. In other words, if you don't know what the call should sound like, you need to hear it first hand, so I'd suggest buying a predator hunting video first and listen, not so much what you should sound like, but more the candence of the sounds. You just need to make sure you sound "distressed".
Coyotes will be where you find them.. In other words, generally they will be hunting for food late evening through the night into the early morning, and then they will lay up for the better part of the afternoon. Now, all bets are off when it is cold or very cold, then they need to eat more and eat more often. SO, early morning or late afternoon, you should try to call them in areas that they likely frequent for food. In the afternoon, you need to call them from thier bedding areas.
Calling them in is the easy part, killing them is the hard part!
Good Luck!