Which version of EyeTV are you using? I know there is a separate Volume control within EyeTV 3.2.1 and it might be able to set from within that application itself.
Note: After launching my EyeTV I saw there is no automatic function. However in the application itself you can adjust the sound (within the application, not the full system sounds) by holding down the ⌘(command) button & either the up or down arrows. This will adjust the sound with the EyeTV application itself.
I guess for something to as automatic as you like would require another piece of software that would have to constantly run, at a great processor rate.