Do you mean stay in the villages or stay with the village people?
Rarotonga is rather crowded with many places to stay around the island. Avarua is the main town but don't expect many 'rooms free'
announces.
Thera are many hostels, hotels, summerhouses and so on. We stayed at the City Motel.
In the smaller islands there are fewer places to stay: on the island Aitutaki I think you'll find 4 - 8 places, from (guest-)house up till a 500 dollar/night hotel! We stayed at Rino's.
The island of Atiu is smaller again and there are only 3 - 6 places to stay. We stayed at the Atiu Motel summer houses.
On the islands Magaia, Mitiaro or Mauke you'll only find one or two places, especially families that offer a room. Perhaps that's the thing you are looking for? I tried to make phone call arrangements with the villagers (take your time while phoning.....) but it ended because at the last moment there was a re-building (... after 3 weeks of several telephone calls).
Perhaps this links can help you more:
http://www.cook-islands.com/openFrames.htm
http://www.cinews.co.ck/
Good luck!
