All the calibers recommedned so far, with the exception of the .223,will ruin a coyote pelt (especially the 50BMG LOL

) so if you are considering collecting the pelts the deer/coyote combo would not be the way to go.
If you are not interested in the pelts, then any of the calibers mentoned will work so why not pick one that is better suited to the deer hunting side of the equasion.
I just bought aRem 7600 in 7mm-08 as my deer/coyote combo. (7600's also come in .243 and .270) Assuming the loads are as accurate in my 7600 as they are in my Rem Mtn LSS, I'll be using a 100 Grn Sierra HP for coyotes andeither 145 Grn Speer SP HotCor (Open)or a 154 Hornady RN (Woods) for deer.
I figure the pumps quick second shot capability will come in handy when more than one coyote shows up at the same time. Doesn't hurt to have it available when deer hunting either.
firstshot
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Make your first shot count!