In Greek mythology, Demophon referred to two different kings: one of Eleusis and the other, Athens
Demophon was a son of King Celeus and Queen Metanira. While Demeter was searching for her daughter, having taken the form of an old woman called Doso, she received a hospitable welcome from Celeus, the King of Eleusis in Attica. He asked her to nurse Demophon and Triptolemus, his sons by Metanira. As a gift to Celeus, because of his hospitality, Demeter planned to make Demophon immortal by burning his mortal spirit away in the family hearth every night. She was unable to complete the ritual because Metanira walked in on her one night. Instead, Demeter chose to teach Triptolemus the art of agriculture and, from him, the rest of Greece learned the plant and reap crops. He flew across the land on a winged chariot while Demeter and Persephone cared for him, and helped him complete his mission of educating the whole of Greece on the art of agriculture.
The other Demophon was a King of Athens who was in Heraclidae, a play by Euripides, starring Macaria, one of the daughters of Heracles. She and her brothers and sisters hid from Eurystheus in Athens, ruled by King Demophon. As Eurystheus prepared to attack, an oracle told Demophon that he would win if and only if a noble woman was sacrificed to Persephone. Macaria volunteered for the sacrifice and a spring was named the Macarian spring in her honor.