Various parents were given for Rhodos. Pindar makes her a daughter of Aphrodite with no father mentioned, for Herodorus of Heraclea she was the daughter of Aphrodite and Poseidon, while according to Diodorus Siculus she was the daughter of Poseidon and Halia, one of the Telchines, the original rulers of Rhodes. According to Apollodorus (referring to her as "Rhode") she was a daughter of Poseidon and Amphitrite, and full sister to Triton. However, for Epimenides, her father was Oceanus, while according to a scholion on Odyssey 17.208 (calling her "Rhode"), her father was the river-god Asopus. Perhaps misreading Pindar, Asclepiades ("presumably the mythographer" Asclepiades of Tragilus) gives her father as Helios. In one source, Rhode was the mother of Ialysus, Cameirus and Lindus.
The poet Pindar tells the story, that when the gods drew lots for the places of the earth, Helios being absent received nothing. He complained to Zeus about it, who offered to make the division again. Helios refused, for he had seen a new island about to rise from the sea. So Helios, with Zeus' consent, claimed a new island (Rhodes), which had not yet risen from the sea. And after it rose from the sea he lay with her and produced seven sons. According to another source, it was Helios himself who caused the water overflowing the island to disappear, and after that he named this island "Rhodes" after Rhodos.
By Helios, Rhodos was the mother of the Heliadae, who succeeded the Telchines as rulers of Rhodes. According to Pindar, Rhodos had, by Helios, seven sons. Pindar does not name the sons, but according to Diodorus Siculus, the Heliadae were Ochimus, Cercaphus, Actis, Macar (i.e. Macareus), Candalus, Triopas, and Tenages. Diodorus Siculus also says that Helios and Rhodos had one daughter, Electryone. A scholion to Pindar gives the same list of sons, with Macareus (for Macar) and naming the last Heliadae as Phaethon, "the younger, whom the Rhodians call Tenages". The older Phaethon referred to here probably being the famous Phaethon (whose story is told by Ovid) who drove Helios' chariot. The scholion on Odyssey 17.208 (perhaps drawing on either of the lost tragedies Heliades (Daughters of Helios) by Aeschylus, and Phaethon, by Euripides), also makes Rhodos the mother, by Helios, of this famous Phaethon, as well as three daughters: Lampetie, Aigle, and Phaethousa. (In the Odyssey, Lampetie and Phaethousa, the shepherds of Helios' cattle and sheep on Thrinacia, are instead the daughters of Helios by Neaera.)