Which support for underneath CD player?

You might try a set of Aurios Pros. They are expensive, but make an enormous difference.

try a $4 small inner tube from a kids bike or wheel barrow with something heavy on top (large book, slab of marble, etc). Its only $4 and probably the cheapest trial method you could do before investing in other methods...

I second Rgd's suggestion, except I'd add try it without the book or the slab of marble as well (just make sure the player is level), as you'd like to drain the vibrations from the player into the innertube as well as those coming from the shelf on which the player sits. You might try the heavy book on top of the player to add damping as well (I found a telephone book on top of a Marantz CD 63 to be effective in that regard). Different feet, shelves, etc. will definitely change the sound, often in a way you might prefer, but with tubed equipment I've concluded after a lot of trial and error that isolation from vibrations is the best route to getting the best resolution and sound. And Rgd's method is very cheap and effective.

Pend there are a thousand opinions on this issue: My own results with inner tubes were not good at all, but it won't hurt to try it. Good results were achieved with a Black Diamond shelf sitting on Vibrapods. Cones are then placed under the CDP in between the BD shelf; BD #4 cones are presently installed, but sometimes the BD #3's or even brass Audio Point cones with saucers are better, depending upon the downline setup in use at the time. Similar setup is under power amp , tuner & preamp, but these are better without cones in my rig (yours will be different of course).
However I found that those glass doors are awful & it all sounds much better with them removed. This was true whether the doors were closed or left standing open

I have had excellent luck with the Machina Dynamica Nimbus isolation base which uses a Firestone air shock as the primary isolation device. The air shock is gravity loaded with 30# of dead weight and the pressure set at 28-30#. Based on my experience with the Arcici airhead, I think that Arcici's approach is rather simplistic and prone to variable results. I find it to be little better than an inner tube (which is exactly what the Arcici is-three or four tractor tire inner tubes in a nice box). If your decide to try this approach, experiment with inflation (less is often better than more) and with mass loading. If your cd player is light, try adding weight to get the total to 30# or more. Good luck.