I have had the center support bearing go bad, and the CV joints in the half shafts on the rear axle go bad over the years on 240D's. They made distinctly different noises, but in both cases you could find a speed and load (how much throttle you give it) condition where the noises would subside.
The center support bearing was a distinctly bearing type of noise, whirring, groaning, droning and the like. It tracked with speed in terms of loudness and tone and seemed to be coming from the driveshaft tunnel. The CV joint noises were much more alarming and also tracked with speed but were not coming from the driveshaft tunnel. Open the window and listen, or have a back seat passenger listen with the rear window open.
Once under the car the condition of the driveshaft center support bearing was visually apparent, the rubber do-nut it sits in was shot and you coud see the races. With the CV joints, there was a low speed, "crackling" type of noise coming when the car was rolled along the street that was clearly coming from the half shaft area. Grabbing the half shaft on one side and jerking it around compared to the other side showed some extra movement. I may have worn the machine more than most, but I was on a 600 mile trip and drove home with the noise, trying to hold the speed and load where the noise was least noticeable. Upon close inspection the boot showed a small tear also and that is the apparent cause of failure of the insides.
1986 Euro 190E 2.3-16 (291,000 miles),
1998 E300D TurboDiesel, 231,000 miles -purchased with 45,000,
1988 300E 5-speed 252,000 miles,
1983 240D 4-speed, purchased w/136,000, now with 222,000 miles.
2009 ML320CDI Bluetec, 89,000 miles
1971 220D (250,000 miles plus, sold to father-in-law),
1975 240D (245,000 miles - died of body rot),
1991 350SD (176,560 miles, weakest Benz I have owned),
1999 C230 Sport (45,400 miles),
1982 240D (321,000 miles, put to sleep)