Shoulder strengthening is great on a BOSU-ball, because you get to work your shoulders as well as your core, while balancing on it. So what you would is stand on the BOSU-ball, with the weights in hand and you can do different shoulder exercises. So one would be a fly out to the side, lateral raise. One would be a front raise, right to the front. You want to make sure your knees are slightly bent on the ball so you have some stability. Another one would just be an overhead press.
Another thing you can do for your shoulders, if you don't have wrist issues is, you can come down into a plank position on your hands and then you take one elbow, you bring it down. The other one comes down and then you push yourself right back up.If you're going to do one side, so my right came down, then my left came down. You want to balance it, so then maybe my left would come up and my right would come up. My left would go down first and so on. Those would be a few good shoulder exercises you can do on a BOSU-ball.