We don't know exactly when Diamond died, but in IV 63, at the age of 94, her husband Peregrin left the Shire and resigned the Thainship to their son Faramir. There's no mention of Diamond associated with this event, which strongly implies that Peregrin was a widower by this point.
2
Diamond's family before her marriage to Peregrin Took is not stated. Her original home of Long Cleeve was particularly associated with the North-tooks, a distant branch of the Took clan descended from Peregrin's ancestor Bandobras, so there's a possibility that Diamond came from this branch. Doubtless there were other families resident at Long Cleeve, too, so an association with the North-tooks is circumstantial at best.