No gold coin is currently illegal to own in the United States. The famous case is the 1933 Double Eagle, a $20 gold coin that was never officially released because President Roosevelt ended the gold standard that year.
The US government ordered nearly all of them melted down, making private ownership illegal for decades. However, a small number survived, and after a long legal battle, one specimen was authorized for private ownership and sold at auction.
Today, that single coin is legal to own, but any other surviving 1933 Double Eagle is still considered stolen government property.