376 B.C.
Well, Demeter and Zeus created her so therefore, Demeter gave birth to her.
Greek mythology does not work according to our chronology. There are no years, no months... No time in our sense of the word. Compare this question: what exact year was our God born!
Most scholars say no, but some ancient sources credit her with 1-3 children, by either Zeus or Hades.
Zagreus is the best known. The Orphic cult said that Zeus raped his daughter in the form of a serpent, and she bore a son named Zagreus. Zeus intended to make the boy his heir, but Hera manipulated the Titans into destroying him. Zeus managed to save Zagreus' heart, put it in a drink, and give it to his lover Semele, thus impregnating her with Dionysus. Some sources name him as Hades' son, rather than Zeus'; some myths also say that Zeus took Hades' form to sleep with Persephone, rather than a serpent's.
Melinoe is said to be his twin; like the Norse goddess Hel/Hela, her body is half black (representing Persephone's chthonian nature) and half white (representing Zeus as king of the gods). Like Zagreus, some say that she is Hades' daughter rather than Zeus'.
Macaria, when she is mentioned at all, is always said to be Hades' daughter; she was the goddess of the blessed dead, presumably the lady of the Elysian Fields.
(Note: I've always felt a very strong affinity for Persephone; if I had lived in Ancient Greece, I suspect I would have worshipped her the most fervently. Stories like these are the reason I don't like Zeus.)
Why couldn't Persephone have kids?
Because as Hades' wife, Persephone is a Goddess of the Dead. All of the departed souls are her 'children', and death cannot create life.
Why does Demeter adore Persephone?
Demeter adores Persephone because persephone is her daughter and the official start of spring
Who is Persephone the daughter of?
Persephone is the daughter of Zeus and Demeter. Demeter had her daughter kidnapped from her by Hades. Then Hermes helped her get her back and they later learns that her daughter had eaten the fruit of the dead (a pomegranate) which means she had to spend 6 months of every year being her Uncle Hades's wife. This story explains the seasons. Since Demeter is the Goddess of Grain and nature on Earth when her daughter is with her (summer and spring) the land is full of great grains and beautiful crops and fruit growth. When her daughter is away (winter and fall) she misses her daughter and the land is very bare. Eventually Persephone turned older and stayed down there full time and she is ironically called the Goddess of anti light even though Hades describes her as a glowing light and he has a realm in hell named after her which consists of the only spot of light in all of hell.
Any of the other Gods and Goddesses of Olympus or the Underworld. Namely Hades, Demeter, and Zeus.