re: 9 year old son. Right handed, left eye dominant.

I've done a lot of gun toting/shooting (close to a million rounds downrange myself) and have taught a lot of gun toters.

For pistols, a cross-dominant shooter needs to do one thing and one thing only - change his/her stance.

Example: A right-handed shooter will typically stand with their left foot slightly forward (not like the old Weaver stance, but like an athlete's stance - say right toe even with left heel or thereabouts.). When you stand like that, your strong side (in this case, your right) hip/shoulder are naturally slightly behind the other, making your strong side/right arm "shorter." Thus, when your hands are meeting on the pistol, it has to be slightly right of center (because your left arm is "longer and your right arm is "shorter"), placing it in front of your right eye.

For a cross-dominant shooter, just switch your feet. It'll make your weak side/left arm "shorter", thus dragging the pistol over in front of your left eye.

That's it. That's all you need to do.

Rifles depend a little more on the sight system - irons, optics (RDS or scopes), peephole sights, etc.

If it's just recreational shooting, then you can get pretty elaborate with how you go about it. For combat shooting - or shooting of any kind where something truly important is on the line - it needs to be simple and repeatable under stress.

And as with anything important, it's about getting reps in.

Edited to Add:

Our vision is best when our eyes are centered up/level in their sockets, so whatever solution you use should minimize deviation.

That's why typically it's best to just learn to shoot on the side of the dominant eye vs. extreme movements (head rolling/tilting, etc.) to get the good eye over on sights that are oriented with the strong side. Some people can pull it off okay, and that's fine. It's just something to consider as you work through it. (Add in low-light and it's even more important since our vision deteriorates anyway.)

We have two eyes to give us binocular vision and depth perception. One of our eyes does most of the "seeing" and the other provides the complimentary information to our brains. The dominant eye is dominant for that reason. You can, with some work, enhance the non-dominant eye or switch dominance.

Instead of a full blown patch, if you want to maintain a "both eyes open" habit, but retrain for dominance, just use clear glasses (which you should be wearing anyway) and smear some vasoline over the eye your current dominant eye. It'll blur the vision and force your other eye to take over, but will allow you to keep both open vs. going dark with an eye patch.