Most visitors arrive by private yacht, and the island sees about a dozen visiting boats a year. There are supply boats that arrive two or three times a year. You could probably arrange to travel on one of these but bear in mind you would be stuck until the next one arrives.
It is generally best to arrive during the daytime. The islanders can then see you approach and will invariably scramble to be the first one to meet you offshore in one of their boats. You will need the assistance of the islanders if you intend to anchor inside the lagoon as the passage is narrow and quite treacherous.
There is a telephone service to Palmerston and it would probably be a good idea to call before arriving. Often the islanders will want specific goods or people brought over and they will be very grateful to you if you can oblige, particularly if you are able to pick up their mail from the Rarotonga post office.