Most likely you will need to remove the rear differential cover, drain the fluid and buy a gasket and/or some black RTV sealer.
Spray something like Penetro90 or rust buster around the filler plug to loosen dirt and grime, and also wipe out the diffy case with a clean rag. Don't freak out if you see some small flakes of metal and grey past, this is normal. Check the gearing with a flashlight and examine the wear patterns. Since you don't have any noise or problems, you should be OK.
Clean the diffy cover and mating surfaces with a solvent and rag.
Place some RTV on both sides of the gasket (a thin film) or if there was no original gasket, place a thick bead of RTV on the case mating surface (especially around the bolt holes), wait a few minutes, and then place the cover onto the diffy case and rebolt. I would wait at least two hours before filling in orer to let the sealant cure somewhat. Retorque bolts.
You will need about three quarts of replacement fluid. Pump the fluid into the case through the filler hole until it starts to run out on its own. Let it run until it drips and then replace filler plug.
Any SAE GL5 75W90 gear oil such as Schaeffer's #267, Amsoil's new heavy duty Gear oil, or Redline, or Royal Purple should suffice. I am sure any of the sponsor's would help you with obtaining the fluid for your application.