On dynamically loaded parts, we tend to use ' loss angle' as a measure of internal damping (hysteresis).
Loss angle is defined as the phase lag between the applied load and the transmitted load through a rubber component, and is to a certain extent, dependent on dynamic amplitude and frequency.
Depending an the application, we also use dynamic stiffness as a measure of damping. Dynamic stiffness is the gradient of the hysteresis loop produced during cyclic loading, and is also frequency/amplitude dependent. Dynamic stiffness is lowest at large amplitudes and low frequncy, and highest at small amplitudes and higher frequencies. Dynamic stiffness is always higher than the static stiffness.
These properties are dependent on material type and composition, but are not necessarily related to durometer.
60 shore natural rubber will generally have lower hysteresis than 60 shore chloroprene, for example.
If you need accurate dynamic data, you will need to perform dynamic tests at a range of amplitudes and frequencies. Manufacturers of rubber antivibration mountings (including the one I work for) routinely produce this type of data.
I hope this helps
Tom