It could be the rubber shock mount bushings, instead of the shock, itself. You might try spraying the rubber bushings with silicone spray. I don't know for sure if that will fix the problem, but it's worth a try. You can get silicone spray at your local auto parts store. A lot of people will tell you to use WD-40 on rubber bushings, but really, you're not supposed to. You're supposed to use silicone on rubber bushings or rubber mounts. WD-40 can cause the rubber to dry rot.
Most 4-wheeler problems are caused by a loose nut connecting the handlebars and the seat!!
You only need two tools in life -- WD-40 and duct tape. If it doesn't move and should, use the WD-40. If it shouldn't move and does, use the duct tape.