I installed an aftermarket (read: eBay) single DIN faceplate in my e39 BMW 540i many years ago. I greatly enjoy my Alpine headunit over the factory DSP sound, but the aesthetics leave a lot to be desired. EBay helped provide a partial solution with a cheap plastic faceplate to help fill the empty space, but it rattles over every little bump! Needless to say, this quickly becomes an annoyance. I finally had enough and came up with a quick fix. All you need is common undercoating, sold at any auto supply store; I think Walmart even carries it. I bought mine at Advance Auto for $4.99. It would also be wise to buy some blue masking tape to prevent overspray.
Step 1) After you have acquired the above materials, thoroughly mask of the sides & front of the faceplate. I stopped masking where I thought the overspray would stop and had to clean up some undercoating afterwards.
Step 2) Score the inside of the back of the faceplate with a sharp knife. This helps promote adhesion of the undercoating and is optional.
Step 3) Spray the back of the faceplate and let dry for 24 hours. Do not touch!
Step 4) Reinstall and enjoy your rattle free car!