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.
You very well might be correct as the Roman coins I have seen were largely illegible.
I was basing my guess on the dates I have seen on early Roman writings, which used either or both the AUC or the years of the Consuls serving at that time,