You can use continuous lights to shoot sports in a studio but you're going to have to up the ISO a lot to get a fast enough shutter speed. A better solution however is to use flash. The shortness of the flash duration when using a flashgun that uses trail trimming (where a transistor cuts power after a certain delay when lower power is required (thus giving a very short pulse)) such as most hotshoe flashes is ideal for stopping motion, and you'll maintain image quality as you'll capture a lot more light than continuous lighting will provide.
You'll lose the ability to shoot at a high framerates, but the action you're trying to capture will most likely be over in a shorter time than the gap between frames anyway, so you're better off working on your timing and shooting the same action many times to get the shots you want.