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.
Interesting article, the thing with diamonds is, that they dont need much to be found, shovel and a strong back. it only takes a miner.
I mean they need a lot of time to find them. Sure if you get a thousand people seraching a river you might find one fast enough... But 1 person could be looking for a while I would think