The '99 E300 belt tensioner has been rattling away for most of a year. First I replaced the belt and entire tensioner assembly, then I did the engine and trans mounts (one of the engine mounts was collapsed but that didn't solve the problem).
Replaced the alternator tonight because it had started to make a whining noise and...duh...alternator bearings were bad and that was causing the tensioner dance. Even though it beat the new tensioner shock absorber to death (just noticed it's been leaking a bit) the belt and tensioner are finally quiet at idle. I kept the old tensioner so I'll put the old shock in for good measure, but it doesn't even seem to need the shock now.
I'm going to tell myself that at 198,000 replacing the tensioner and mounts was a good idea anyway...