Good question. There is a second-hand diamond marketplace. But the discount you get is proportional to the extra effort you must exert to get the diamond you want. Do you want a 2 carat triple-A GIA certified round brilliant with VS1 clarity, >I color, and an HCA score under 2? Good luck. You'll spend months tracking that down. And you better know what you're doing or you could get scammed. Or you could go to a diamond wholesaler and get what you want, right now, no hassle, and pay the associated overhead.

So there's an opportunity here, for a market facilitator. Hire a few qualified gemstone appraisers, set up an auction site and take a small rake off the top.

Such places exist. I know of one (http://eragem.com/) but I'm sure there are others.

The euphemism "Estate jewelry" instead of "secondhand" or "used" seems to be preferred.

Even better, write some image-processing software that can automatically grade diamonds more quickly and accurately than human appraisers.

Diamonds are already largely graded automatically. DeBeers has invested heavily in grading equipment that can specifically distinguish natural from artificial diamonds.