It'd have to be a big private yacht, as Pitcairn has no sheltered harbours.
For a small yacht, even in the lee of the island, it would be difficult to stay for long, and you'd have to be prepared to leave whenever the weather changed.
Many smaller one-person yachts visit the island, they anchor offshore and get transport to the island via the islanders coming out on the longboat. Yachties stay overnight on their yacht for safety reasons - there have been incidents of them breaking away from their anchor.