There are no jobs per se available to non-residents, only a few professional services e.g. teacher, nurse, social worker hired by the government in New Zealand, and a pastor assigned by the international Adventist church. On the other hand, anyone taking up temporary residence on the island is expected to be self-supporting, and to help with community needs such as crewing the longboats to reach supply vessels.
Sail yourself or perhaps travel with the locals to another of the islands. Oeno has sandy beaches suitable for swimming, Henderson offers rare opportunities for birdwatching and exploration of ancient caves dwellings?, and both are good for snorkeling or scuba diving among coral reefs and a few shipwrecks. Ducie is over 300 miles away, out of range of the islanders' boats, and therefore rarely visited, but is also good for seeing rare birds.