I think Dextron is your only option

What kind of noise does it make? When I had no fluid in my healthy A131L diff it made a bit of noise, but the tranny was pulled at the time.

 

Noise is usually caused by wear on the gear, changing the fluid most likely won't make any difference in the noise. I used Eneos "ECO-ATF" in mine simply because that was what I was using in the transmission. Eneos claims this product is Dexron III compliant, which should also be Dexron II compliant.

In hindsight it may not have been the best choice because full synthetics like this can leak through old seals, and a differential without any oil in it is downright dangerous. If you choose to go this route, just keep a close eye on it. So far I haven't ran into any issues, and that was about a year or two ago that I changed it.