Vibration from rear wheels / axle when accelerating

When accelerating at a normal rate, and whether the car is in automatic or sport shift (manual) mode, I get a vibration (feels like from right rear more than left) which feels and sounds like going over a rumble strip between the speeds of twenty to thirty mph and most noticeable in second gear. I have had tires balanced and rotated and vibration still stayed in the right rear area.