The Blue Lagoon

The Blue Lagoon by H. De Vere Stacpoole.  

The story centers on two cousins, Dicky and Emmeline Lestrange, who are marooned with a galley cook on an island in the South Pacific following a shipwreck. The galley cook, Paddy Button, assumes responsibility for the children and teaches them how to survive, cautioning them to avoid the "arita" berries, which he calls "the never-wake-up berries."

Two-and-a-half years after the shipwreck, Paddy dies following a drinking binge. The children survive on their resourcefulness and the bounty of their remote paradise. They live in a hut and spend their days fishing, swimming, diving for pearls, and exploring the island.