Many people have found mass damping their CDP's to be a positive thing! One thing you could try very inexpensively... Pick up three or four 1" superballs at your local dollar store. Cut them exactly in half and spread them out evenly on top of the CDP. Remove the original feet from your tape deck, if need be, and place the deck on it's new feet. The balls should help dampen out vibration.
Have fun!
Have fun!