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".)