I had the same problem with my sewing machine on a folding table. Like you I couldn't find anything at the thrift store then i saw an ad in the paper for a computer desk with a door for storage on 1 side and 3 drawers on the other was a really cheap price so I bought I. No more problems with shimmy and shake, use the keyboard tray to store my scissors, clippers and seam ripper so they are always at hand.
Jane Sisk