My own experiences mirror Keiths.
I havs shot coyotes with 17HMR, 22Mag, 22 Hornet, 223, 22/250, 357 Maxi, 8MM Mauser, 454 Cassull, 12Ga and my bow. one of the ones that ran the fartherst was one of the last ones shot... the 454 with a speedy 200g FTX bullet at about 30 yards. Hit broad side thru the lungs with close to a 4" exit....
The 17 was head shot and DRT, the hornet has the most and that was out of my Contender. 46G HPs and 40G Speer bullets doing a good job on anchoring them. The maxi, Mauser, 12Ga and bow where all kills when deer hunting and thats what I had to shoot them with. The 22 Mag, 223 and 22/250 where specfically for coyotes and worked as one would expect. I know I shot at least one with a 40g HP from the 22/250 and the bullet blew up on the sirface. Making a softball sized hole high on the shoulder, about 1-2" deep. The dog screamed and began spinning, my buddie hit him again and he went down.
If I was needing a long range gun your 25/06 or a 243 might make a fine choice. If its what you have, it will be just fine for any yardage.
My self, I am going smaller... Uncharted territory for me as I subscribe to the heavy for caliber slower moving bullet theory. IE Torque over horse power... I am building 17 Hornets for coyotes... 20G bullets at 3600+ fps. We will see how it preformes..
CW