Well if you want to cut out the middle man, I would suggest looking at the cryptocurrency VeChain as it hopes to make the supply chain of a product more visible.
And yes it would be amazing to do that.
But with Debeers owning more than enough diamonds to supply the world, and lab grown diamonds coming into existence this may not be the trade to enter.
You might be interested in this article which talks about tracking the sale of diamonds through the Bitcoin Ledger. Though a quick switch monero would make this useless.
RE: Diamonds with bitcoin the knot