The unknown penitent, presumed to be the thief himself, asked the priest to return the loot to the Paestum archaeological park near Naples.
He insisted the coins had to be given personally to the site's director Gabriel Zuchtriegel, the park said in a statement.
“It's the latest restitution by someone who feels remorseful” for stealing things, the statement added.
Of the 208 coins returned, seven were fakes but most of the others date from as early as the third century BC, running up to the end of the 4th century AD.
Paestum, originally a Greek colony that was later conquered by the Romans, boasts three of the best preserved Greek temples in the world.
It is not unheard of for people to return artefacts stolen from Italian archaeological sites, sometimes after decades.
The former manager of Pompeii, the ancient Roman city, said that in recent years the site has received around a hundred packages returning stolen relics, which are often accompanied by letters explaining that the items have brought the thieves nothing but bad luck.
Remorseful tourists also sometimes return sand stolen from the pristine, protected beaches of Sardinia.