Well, the traditional harder-than-gold precious metal would be platinum. I seem to recall seeing some titanium rings, but titanium isn't really all that hard, though far harder than gold, silver, or platinum. But you could be Mr. Cool and get someone to construct you an iridium ring or something.

Huh. Actually, it looks like many platinum rings are alloyed with iridium or ruthenium. Check those out. Here's some relevant information.