The 243 savage will fit the bill nicely for what you are using it for. I've killed 2 of those Nebraska deer with my 243, and probably 40-50 other deer with the lil 243, and I've only had one take a step. I worked up a max load pushing a 95gr Combined Technology BT, and they anchor deer very well. In fact, I shot one of those Nebraska mule deer at a lil over 400 yards.
For coyotes the best combination for a fur friendly load I have found is a 60gr Sierra HP @ 3600fps. Anchors 'em in their tracks, and will not exit with a rib-cage shot. If you hit the shoulder blade it could get ugly, but I've only had to throw out maybe a handful of coyotes shot with that load out of well over 100 dogs.
In fact, here is my new coyote/backup deer gun:
That coyote didn't like the 60gr pill yesterday
