I am looking around for a decent small caliber gun for coyote and possibly to carry with during deer season also. I am trying to mix the two and have it narrowed down to a few different calibers.. Ballisically the best I have chosen is the 25-06 but is this over kill for coyote with 100 grains? The other 2 I would try would be a 243 wssm or a 22-250. But the 22-250 I wouldn't be able to shoot deer with.

the 25-06 is plenty for coyotes, and you will have pelt damage. BUT probably no more pelt damage with your soft points than the 22-250 has with 50 grain BT bullets!

Unless you are keeping the hides, there's no such thing as overkill. If you are keeping the hides, a .222 or .223 would work better. But if you use a solidly constructed bullet like you would use for deer, you can still probably salvage most hides with a .25-06. May have to do a little stitching and may ruin a few, but that's just a price you pay to coyote hunt with a deer rifle.