Cozumel ( Mayan : Island of the Swallows ) is an island in the Caribbean Sea off the eastern coast of Mexico 's YucatÃ n Peninsula , opposite Playa del Carmen . Cozumel ( Mayan : Island of the Swallows ) ( KÃ utsmil in Modern Maya ) is an island in the Caribbean Sea off the eastern coast of Mexico 's Yucatan Peninsula , opposite Playa del Carmen , and close to the Yucatan Channel .