Please be aware that Rome has multiple airports and that these results are for all airports serving the city.
The best month to fly between Rome and Athens is September and the most expensive month to fly is March. (Average prices, based on 205 datapoints.)
The best day to arrive at Rome is Saturday and it would be best to avoid Tuesday, as prices are on average 155.18% higher than on Saturday. (Average prices, based on 205 datapoints.)
The best time to fly is at around 22. (Average prices, based on 262 datapoints.)