Everywhere I look, when it talks about the plays or wars or anything it just lists the modern calendar dates. I can even find lists of the months, but I'd like to find a resource where it would say, for example, Dionysia in 490BC took place during the year of the 3rd Olympiad or the 2nd summer of the Persian war, or whatever it may be.
I can find some mentions that they would in fact reference years according to the Olympiad, but unless something remarkable happened that year they rarely mention both which olympiad it was and what year it took place according to a modern calendar.
Many thanks in advance!
There are some previous answers that should be helpful:
How confident are we that the year is actually and exactly 2016? Is it possible that at some point in the last 2000 years there were any significant timekeeping mistakes? and Did people in the Middle Ages call the year "one thousand and one" or "ten oh one"? by u/sunagainstgold
At what point did society begin referring to the year in modern terms (2012 etc)? by /u/Algernon_Asimov
And two answers from me about Greek calendars using the Olympic games as a reference point and What year did Plato think it was?
A good resource for Greek (and Roman) dates and how to calculate them is Alan Samuel, Greek and Roman Chronology (Munich, 1972).