Some are suggesting tape that is designed and sold for the exact purpose: on your lathe. Others are fond of some other tape, which if you find a good one, may work well for you. I will just suggest that you pay attention to something if you experiment with tape that is other than the stuff designed and sold for the faceplate mounting. Some of the tape products are fairly thick and (to use a highly technical term) gooey. These type of tapes will hold quite strongly, but because of the thickness of the adhesive they may allow the work to gradually shift. It will still be stuck well to the faceplate, but can drift off-center a little. That can ruin your project, or at least cause it to end up just a little different rom what you intend. Food for thought...