Well, I came accross the Fiji Visitors Bureau website in a magazine this afternoon http://www.bulafiji.com
, and going to it, it appears that the only non South Pacific, non-AirNZ/QF airlines serving the country now are Korean and Air Marshall Islands. Ansett International used to serve, as apparently did JAL. The other one which has escaped everyone here is the late Canadian Airlines, who I believe used it on the YVR-HNL-NAN-SYD routing before they had long enough ranged aircraft. I checked at aircanada.com, and they don't fly to Nadi anymore.
Still looking for info on other islands,
"So powerful is the light of unity that it can illuminate the whole earth." - Bahá'u'lláh