I just read an article in the Jerusalem Post that quotes a 13th century Rabbi saying that Esther’s son was named Darius.
I am not real familiar with the exact period of time that Ester lived and affected the life of the Persian King but I believe it was during the time of the Babylonian exile. Is it possible that this Darius is the same king that gave the order to rebuild the Temple?
If Esther had a son named Darius, as Jewish tradition suggests, he would not have been the same Darius, called Darius the Mede, who helped the Persian King Cyrus conquer Babylon and free the Jews in 535BC to rebuild their Temple. According to Ezra 6:15, the Temple was completed in 516BC.
The Book of Esther tells of events that took place just prior to the very first Feast of Purim, which Esther 8:12 places on March 7, 473 BC, 43 years after the Temple was completed. The Persian King she married was Xerxes I, who reigned from 485 to 465 BC. He was the son of Darius the Mede.
The Persian King who gave Nehemiah permission to return to Jerusalem and rebuild the city walls in 445 BC was Artaxerxes Longimonus. (Nehemiah 2:1) He reigned from 465 to 424BC and was the son of Xerxes I, but it’s not clear if Esther was his mother.