I'm cross dominant and was taught to shoot left. It's the most natural thing in the world for me now. I'm 31 and truly have to make an effort to shoulder a rifle right handed. Since I was younger than your son, I shot left and haven't ever tried to shoot right. Once, with a bow, I tried it and missed by many feet at 10 yards.
In order to aim and shoot well, you must use your dominant eye. You could retrain him to use his right eye, but that would be akin to teaching a left handed kid to write right handed. He is the way that he is, deal with it and accept it. There are plenty of lefty rifles out there, I just don't have any. Never needed one. Pumps, levers and single shots are good options as are autoloaders, if you can't find a lefty bolt gun.