I would guess the date was numbered counting forward from the founding of Rome(about 753 BC), AUC (ab urbe condita).
I don’t think there are any examples of Roman coins dated from the foundation of the city. There are some imperial coins which can be assigned to a particular year because of the titles (usually very abbreviated) given to the emperor. There may be some which say how many times the emperor has been consul or has held tribunician power (which was a kind of regnal dating)—I’d have to consult a book on Roman coins to be sure.