hahaha I am in the middle of this right now. If you don't have a press and a bearing separator like this:
Proto 4332 Gear/Bearing Separator 4 3/8 in #2
you'll need to bring it to a shop to have the bearings removed and repressed on the pinion shaft. How do you know it is the pinion bearings (inner or outer) versus the differential bearings? The diff bearings are much less expensive.
Also, is this a new differential? Was the backlash checked on it? The ring gear could be running too tight to the pinion gear.