The carrier is preloaded with shims. They have to go back in the right way or your backlash will be wrong. There is very little difference in the thickness, they look the same, so it is really important to understand what you are doing if you take it apart. I would probably check the backlash with a dial indicator after it was reassembled to make sure it was within specs.
Are you sure you have ruled out all the simple solutions? Like UPS said, check the wheel bearings. Also, are you sure it isn't a drive shaft problem? If you have ruled out everything else it may be in the rear end, but the pinion bearing usually fails because of inadequate lubrication before the carrier bearings. I would invest in a repair manual before I tore into the rear end too deeply.