Yes, you can mine diamonds in the US. Check out these videos.
Crater of Diamonds History
(I have read that 500,000 people go here each year to grub around in the dirt and look for diamonds)
Arkansas Mining- Crater of Diamonds
More of Arkansas Mining
Diamond Dennis- diamond finds
Crater Of Diamonds 100 carat Club
Herkimer Diamonds New York
(These are not real diamonds but really doubly terminated quatz crystals. Thouands of people go ehre each year to look for thse "diamonds".)