I was just discussing a rear end clunking noise with Greasybenz, we took a drive in my '87 project car. We both drive '87 300D's and we both have a decided clunk when the trans shifts.
One cause for this is worn bushings in the rear control arms, its very common in that chassis. You simply replace the arms. The rear suspension in the W124 need these parts otherwise the cars won't handle right and will make all kinds of nasty noises.
There is a lot of torque in that engine that also causes rubber in the diff mount to flex, its worth inspecting also.
I would put my bets on parts other than the differential, not to rule it out completely but suspension parts are much cheaper to fix than a new diff.

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'95 E320 Wagon my favorite road car. '99 E300D wolf in sheeps body, '87 300D Sportline suspension, '79 300TD w/ 617.952 engine at 367,750 and counting!