Casting Elastomers as Acoustic Insulators
Dampening is actually more complicated than what you're asking.  It isn't simply a matter of using a material that dampens vibration. It's a function of the frequency you want to dampen. You will dampen some frequencies, but amplify others, and can get resonance that's more problematic than having no damper at all. If the dampers will be supporting weight, you also need to consider things like how the compression will affect it. 

There's actually some physics involved in designing dampening to do what you want.  If you don't have access to a physicist or engineer who deals with this stuff, your best approach would be to play with different materials, sizes, etc., to see what works best for your application.  Another option would be to use commercially available dampers that have been designed for your application and that users have said works well.