There is no diff cover on our classics...just two plugs to remove to drain the oil...makes it a simple drain and top off operation.
What to do is remove the bottom plug first...then right after remove the one on the front face to aid in the draining. If you want, you can use sealant tape, for fittings on the threads of the plugs, once you've cleaned the plugs, to prevent future leaking.
Put the bottom plug in tight/snug. Then top off the diff with either 90W gear oil, or 80W (both have different protection temperature ratings...but in the dead of summer, I'd go 90W. Fill the diff til' the level in the gear oil reaches the level of the fill plug. Tighten the top plug, and that diff is done!!
Repeat for the other diff. Hehe, damnit I gotta do mine still.

It will stink, that's for sure, in smell that is.
Oh and there is no need to use any kind of cleaner, that will not be good for the gears.
Almost forgot...there is no easy way of cleaning the interals of the diff as far as the gears are concerned...they don't really create sludge like the engine does. If one really wants to clean the inside of the diff and the gears, they'd have to pull the carrier which is a really big task...and is not practical. Unless you're swapping gears to a different ratio, which of course requires you to remove the carrier, cleaning is not needed.

__________________
Pat Albaugh, Midwest Moderator
"Diffage" -the point at which the truck's differential makes contact with the ground.
http://www.cardomain.com/id/RageRover42Visit my RRC and others here!(updated as of September 15, 2006)
1995 RRC LWB
-LT265/75R16 Pathfinder All Terrains
-RTE 2" Lift Springs
-Pro Comp ES9000 Shocks (from DAP Enterprises)
-KMC Front Diff Guard
-4 Desert Fox 55 watt Lighting
-Radio Shack CB Radio (never know when signal fails on a cell phone)
-2 Halogen Super Sport 100 watt forward lights
-Brush Gaurd, meant for a Jeep Grand Cherokee, now fitted to the RRC
-Lowe's Special "Homemade" Snorkel
-T-Case out of an 92' RRC