From the Super Mario Wiki
Silver Diamonds are valuable treasures in Luigi's Mansion. Luigi often finds these in Treasure Chests, with two Gold Bars, after completing an optional gallery ghost in the Mansion. Each Silver Diamond is worth 2,000,000G.
In PAL versions of the game in The Hidden Mansion, Speedy Spirits and Golden Mice always drop a Silver Diamond when defeated. It is impossible to get an A rank in PAL versions without going into The Hidden Mansion and getting some of these, as the requirement for an A rank in the PAL versions is 150,000,000G (as opposed to the 100,000,000G in other versions of the game) and the maximum possible amount to get in the normal mansion alone is 142,390,000G. There are a total of 5 Silver Diamonds in the entire Mansion. (30 in the PAL Hidden Mansion)