I had to choose when I bought my coyote rifle but I went with a .223.

If you are shooting them just to shoot them your 25-06 is more than good enough (heck so is your 7mm). I've taken more with my 7mm RM during deer/elk hunting that I have with my .223.

But if you prefer to have a predator-only rifle you just can't go wrong with the 223. Ammo is very affordable, especially lately, and mine shoots so well I can't imagine a need for anything better. If you wanted to hunt predators (coyote, bobcat, as well as groundhogs or marmits) all the time you may be better off with a 22-250 or 220 swift as they are slightly flatter shooting. But much more expensive too. And as mentioned, the 204 may be a little light for song-dogs, especially at longer ranges. I've never had to shoot a coyote more than once with my 223 so it works plenty fine for all my encounters.

Good luck and congrats on the new rifle no matter what you get!