I changed all four tyres on my Toyota Wish about two years ago. Since the change, I have been experiencing a rather frustrating problem. When I accelerate the car from 50 to 55kmh, the front tyres rattle a little, as if they were going over an uneven surface. It also happens when I accelerate from 80 plus to 90kmh. At other speeds, the tyres perform quietly. I've done wheel balancing, wheel alignment and tyre rotation. I also changed the front drive shaft last year, but none of these seem to have resolved the issue. My car has clocked about 70,000km.
The tyres are unlikely to be the problem, since you have already balanced them and the symptoms appear only when you accelerate at the two speed points you specified.
Normally, this is caused by worn drive shafts. You should first check if the replacement drive shafts were brand new or re-conditioned.
Re-conditioned ones usually work reasonably well, but once in a while, you may end up with a problematic set.
If the drive shafts were brand new, then the only places left to look are your car's engine and gearbox mountings.
At the mileage you mentioned, it is not unusual to have broken mountings, which can cause the symptoms you mentioned.
SHREEJIT CHANGAROTH, a regular contributor to Torque, a motoring monthly published by SPH Magazines