Fiji private island trips

Hi.
I've searched for this topic but can't find anything and I've even googled until my eyes are blurry but getting no answers.
I'm going to Fiji in December with my partner. I'm looking to spend a day on a private island, just the two of us, for his birthday. But the only thing I can find is the yasawa Islands (very expensive), turtle island resort (who require a 1 week minimum stay) or a Fiji boat hire company who can arrange it but after 4 emails they still haven't got back to me.
Does anyone know anywhere where this is possible?
Thank you

What do you mean "private island"?
Nanuya LaiLai is the next Island north from Turtle. It is privately owned, half by the resort. The other half was owned by Blue Lagoon Cruises, but they are gone so don't know who owns it now.
http://nanuyafiji.com/
It is much more affordable than Turtle, but is popular, so book ahead.
It only has about a dozen rooms and is owned and run by a local family. One of the few resorts that we would go back to on multiple occasions while we lived in Fiji for 2 years.

Cheers,
Peter

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