For a good all around coyote killer it is hard to beat the .223.
But their are so many other choices,218 bee,223 Wsm,22-250,.222,220 swift,243 win,.243 WSM,6mm,25-06 rem on and on.
What you need to decide is this going to be a cross-over gun,ie deer and antelope.
If this is the case I would go 25-06,good in the wind and deadly on coy-cogs and deer size game.

If not I would go with the .223,ammos cheap,acurate and deadly out to 350-400 yds.

And if you can' t decide you can be like me and own a .223,22-250,.243,6mm and 25-06,why?I geuss more the merry.
Any rifle in these calibers with a good 4-16 scope and a good rabbit call and you are in luck.BBJ