I had the same problem. Here is my cheap and quick fix. I put some JB weld (the epoxy glue) where the stock bracket connects to the lip on the UZI. (I put the glue on the stock, not the gun). I think I unscrewed the bracket from the stock before spreading the glue, if I remember correctly.
After letting it dry overnight, it is a simple matter to use a small file on the glue to a point where it fits tightly. Just keep trying till it fits tight. No more wobble for me. Mine was very loose before.
While it may not last forever (mine has lasted quite well over many months), it is easy to do it again, if necessary.