Hi Nick:
Take a close look at this picture. You'll see that there are two rails on the bottom, in this instance they're curved downward, and attached to the router are two "skis" that match the curve of the rails. The craftsman was creating a curved face for a speaker.
Your jig will require a circular base, two concave rails and two convex "sabot" attached to the router, like skis. The circular base will allow the rails to be rotated around one centre so you can carve all facets. Mount your workpiece(s) inside the circular base.
You will need to use a rounded bottom cleaning bit. I've attached a picture of Lee Valley's "dish carving bit" If you can, find a bit that has a complete round bottom instead of the flat bottom of this one. The size in this picture ain't bad. Some of the "ball" bits have too pointed a bottom and core box bits share the same problem.
Next, you'll need a good curved scraper. The second picture is of LeeValley's "super-hard curved scraper sets." If you have access to good hard thin steel, you can grind your own to match your specific profile.
This is method #24 of 25 methods for router usage.
I hope this helps.