Nothing wrong with the 25-06 for either coyotes or whitetails. There are probably a dozen other calibers that would also fit the bill nicely. You are buying a brand new rifle and want it to be suitable for a beginning youth (I assume) hunter.
A couple of questions:
1) Do you handload or plan to for this rifle? If so, there are choices I would consider better overall than the .25-06. If you are going to shoot factory ammo exclusively, then you are going to be hard-pressed to flat-out beat the 25-06 for both uses. If you handload, the 6.5x55, .270, and 7mms (several) offer a much better range of bullet choices in the deer-sized bullets (125gr +).
2) How recoil-conscious is your son going to be? If this might be a problem area, I would choose one of the lighter-recoil calibers like the .257 Roberts, 6.5x55, or 7mm-08. They would certainly get the job done, but without the heavier kick and blast of the @2,900+ feet per second calibers.
I would second Zachary's opinion that the .243 is a little too light to be recommended for deer. It can be a very good deer killer in the hands of a good marksman inside 250 yards, but it leaves a lot less room for error on either bullet performance or shooter accuracy than many of the other choices. It sits on the very low end of the deer spectrum in my opinion.