There is always caulk, but I would for sure heed these experts advise and tell us the source of the leak.
If its...
A) Leaking from the bottom of the cover, then remove the cover, scrape, get new gasket and clean everything while you are at it.
B) Leaking from the pinion (driveshaft connection) then you need to remove the large nut, replace the seal and if there is pitting on the pinion, add a sleeve.
C) Leaking from the axle (one side or another as evidenced by gear oil on and around the hub, replace axle seals and bearings on both sides just to keep yourself from doing it again soon.
No matter where the leak is, take the opportunity to decide if its time to look at other seals and bearings that could bite you sooner than later. A reputable shop will suggest these things but don't spend more than you should. Hope this helps!
