It depends on the weight of your CD player. If the Townshend seismic platform will work with the weight (they have like 4-5 different tensions for the podiums), I feel that is the best vibration control product out there, but you have to make sure you are isolated from footfalls, which it does not help, so if you have a suspended wood floor, you could experience them, although I suspect not nearly as bad as with a turntable. So as long as you are not walking near it, you should be OK.
Symposium rollerblocks or a platform would be 2nd choice. If you call Peter, he will guide you. I don't have a cd player, but he told me the improvement with his products on a cd player is even greater than a turntable.