Diamonds are valuable on earth primarily for their rarity.
As it turns out, they may not be rare in other places. There may be icebergs of diamonds floating in seas of liquid diamond on Neptune and Uranus. http://www.popsci.com/science/article/2010-01/diamond-oceans-may-cover-neptune-and-uranus
I wouldn’t think there’s be much economic value, though. Let’s suppose investors funded a robot expedition to Uranus, and many years later a couple icebergs of diamonds made it back to earth. This would flood the market, making them no longer rare or worth as much. Let’s face it – if people wanted them because they are sparkly then we’d all be buying cubic zirconia.