I prefer Diana as the only child that grow up on Themysicra.
The Amazons are unaging, but bunches of them do get killed off every now and then, which creates a population question. My solution, tied to Perez's origin of the Amazons, was this: every 1000 years or so, the Greek goddesses take a new group of souls from Gaia's Womb and incarnate them as a new set of (adult) Amazons on the island. That way we get a little variety and differentiation added in: the Amazons who were there originally, the ones who joined in 1000 years later, and so on. It adds a feeling of generations to the immortal Amazons, and might have some interesting social or even political ramifications.