Fake/Counterfeit Coins

Grand tour fakes and fantasies of ancient coins were being fobbed off to unsuspecting tourists as early as the 15th century. Circulating counterfeits and forgeries are virtually as old as coins themselves.

600 BC.

The earliest coins were made from the dubious Au/Ag mixture electrum. The gold content was not controlled, but over 50 years relatively pure Ag and Au coins appeared. Still electrum never went away, and was used for coinage for several hundred years all around the Mediterranean.

One of the earliest counterfeiting techniques was called fourree, or "stuffed". A base metal planchet was wrapped with a thin foil of a precious metal before striking. From wiki,

"Production of fourrees began almost as early as the production of the first coins in Asia Minor in the 7th century BC."

@Hunter611, Virtually all coin series will attract contemporary counterfeits - US 19th / 20th C. coinage was no exception. So the answer is soon after the coins appeared in circulation. Numismatic forgeries (altered mintmarks / dates, fakes of rare types / dates) were already known for the Morgan series at the turn of the 20th century, so also basically contemporary to the issues themselves.