There are 2 bearings on the pinion, and should both be replaced if replacing any bearings at all. Just because there is some play doesn't mean the bearing is no good, the nut simply could have backed off a bit causing the play. You need to inspect the bearings first of all to see what needs to be replaced if anything.
To do so you will need to drain the differential, remove the cross pin retaining bolt, the c clips and pull the axle shafts out. The carrier bearing caps need to come off, mark them so they go back on the same side they came off of and in the same orientation. Remove the carrier from the housing and make sure you keep the shims in order of which side they came from. Next you will have to remove the pinion nut and remove the pinion from the housing. You can then inspect the bearings for heat marks/pitting and scoring and see if anything needs to be replaced. The bearing closest to the pinion nut simply slides off, the one close to the pinion head is pressed on and there are shims underneath it. The bearing races need to be removed from the housing using a drift and hammer. Once the bearings are replaced with the shims all back in the same spots they came from you can reinstall the pinion into the housing. You will need a new crush sleeve and pinion seal. You will need and inch lbs torque wrench to set the pinion bearing preload. Once you get that back in spec you can install the carrier with the shims in the same spots you should put some gear marking compound on the teeth of the ring gear and run a pattern check. If all looks good you can refill and you're done.
