i've used the redline diff oil. the same weight as the hand book states (think its 75w-90) off top of my head. But get one that has additive added already and one that doesn't. The diff should take both so its still got additive in overall. Assuming you have clutch type posi rear if it chatters too much or locks out not to your aste you can put more additive in to make it 'slip' a little more.
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'99 Z28 A4, 253 LS2 heads, 228R TSP cam, Patriol Dual Springs, Double roller timing chain, LS6 ported oil pump, OBX LTs, 3" True Duals, LS6 intake, 42lb/hr injectors, SLP lid + bellow, EFIlive COS 3 Speed Denisty Tune (self tuned), 3200 Circle D stall, CAI mod, KYB AGXs, Eibach Pro Front Springs, UMI panhard, LCA + Brackets, Strut Brace, Custom Subframe connectors, WS6 axle with 3.42s, 18" American Racing Rebels, US mirrors, 93 tail lights, 3.5 inch custom cowl hood. Mickey T's Street DRs on Vette-ZR1 wheels for the strip !
Best ET: 12.0 @ 116 mph (on a 0-60ft of 1.8 s)