They wouldn't. Diamonds are actually already extremely common on Earth. The perception that they're rare and therefore should be valuable is partially because that was true in the 19th century when mining and (Can't think of the word for it...searching for mineral deposits) weren't good enough to mine a significant amount of diamond. But they are now. Once diamonds started to become really common, the largest of the diamond companies banded together and created De Beers Jewelers [http://www.debeers.co.uk/?region=true], forming a monopoly over the diamond market and allowing them to control the prices. Then they went and advertised diamonds as being rare and very valuable, when in reality, they're almost worthless.
Funfact: Despite being based in the US, Rhodes, Beit, and Rothschild (The founders of De Beers) refused to set food on US soil for fear of being arrested as soon as their plane touched down because of how blatantly illegal what they were doing was. They also had a few more controversies surrounding them, like refusing to help the WW2 war effort (Which isn't supposed to be optional)