About forty five years ago this was my answer to a dominant left eye, rest your top lip against the exposed stock bolt and you can also have your head positioned perfectly for each shot.
Caused a bit of ribald comment at the match small-bore indoor rifle club I belonged to at the time. Didn't improve my scores either. Where as the top shooters were getting a perfect score most times I could never do better than ninety eight out of a hundred. Very little room for error in this discipline.
I now realize that even though these rifles are the tops for accuracy they are still sensitive to the ammunition which are run through them. Didn't realize this just starting out in shooting and assumed that what the the other guys were shooting should have shot ok in my rifle.
These days I now personally wouldn't bother worrying about a dominant eye in rifle shooting.
Since I have had a cataract done in my right eye and the sight picture is sharp again and at the age of 74 I came out top at a recent 300 metre iron sight shoot.  
My first rifle and I still have it, although its now in K Hornet and great for head shots on rabbits destined for the pot.

Please don't burden him with goofy stocks and sights. As long as he has two good eyes, he can self-correct the issue. 

My grandad recognized my cross-dominance issues many years ago and began working with me to deal with it using instinctive archery technigues because it was something I could practice daily in the back yard. At first I used an eye patch - then learned to close the left eye - then only slightly squinted the left eye. Eventually, I could do just fine with both eyes wide open. Now, many years later I don't ever think about it. If my left eye ever tries to "take over", I automatically blink and the right has control again.

1000s and 1000s of arrows flung at a target was fun therapy and a very practical "cure".  It will aid in making him a quicker game shot with the rifle and a faster learn with the shotgun. Besides all that, it will introduce him to the relaxing and enjoyable outdoor activity of archery.

xtm

Thing to consider when correcting for cross eye dominance is your eyes will change as you get older.  Simple shading of the dominant eye works and can be switched to the other eye as it changes. Or in my case using the dominant eye for pistol shooting off eye for rifles.   

Brian Enos one of the best speed pistol shooters ever shades his off eye with scotch tape. David Tubb best rifle shooter of our time does the same thing.

Boats

I started shooting right eye, even through i'm left handed, it was the way i was taught by my dad(dead about twenty years now).However, it soon became evident to me that my left eye was much stronger so i soon switched to left hand shooting.This was only a problem when shooting bolt action rifles.But when i switched to single shots it was not a problem at all, except i have learned not to use a checkpiece, as these alll nearly right handed.The only single shot that i ever owned i couldn't  use left handed was a german schuetzen martini in 8.15 x 46R.I soon found out i could not afford to restock it, so i sold it sadly.Lovely rifle, best trigger i ever saw.Even through i couldnt shoot it, i wish i still had it, just to look at.

Again, thank you all.

This has been a very informative post for me.  I am right handed and have been right eye dominant until sometime in the recent past. My wife and I took an NRA pistol class recently that checked dominance and all of a sudden I am left eye dominant.  No eye surgery.  No special reason that I know of beyond hitting my 60s.

My main shooting is rifles.  Pistols are a sideline so my wife and I can shoot together (she much prefers pistols and is better with them than I am).  Since I'm not inclined to grind the cheekpieces off my right hand Ballards, I think I'll follow the advice Boats posted.

It really is great to have this forum available to learn from a lot of great, experienced people.

FEB