Here's information from the catalog and the sheet music cover, viewable at Mississippi State University:

THE MOON OF MANAKOORA
Words, Frank Loesser. Music, Alfred Newman.
Hollywood: Kalmar and Ruby Music Corp., 1937.
"As introduced by Dorothy Lamour in Samuel Goldwyn's Production 'The Hurricane'"

First line of verse: Here we stand once more upon the sand, of Manakoora
First line of chorus: The Moon of Manakoora filled the night


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You can hear this version at YouTube:

MOON OF MANAKOORA
As sung by Dorothy Lamour

1. The moon of Manakoora filled the night
With magic Polynesian charm.
The moon of Manakoora came in sight
And brought you to my eager arms.

2. The moon of Manakoora soon will rise
Again above the island shore.
Then I'll behold it in your dusky eyes
And you'll be in my arms once more.

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Actually, only an instrumental version of THE MOON OF MANAKOORA was used in the soundtrack of "The Hurricane," but the vocal recording was released as an obvious tie-in.

There actually is a Manakura Island, one of many islands in the estuary of the Essequibo River in Guyana, South America. That would mean it is not part of Polynesia. Apparently the filmmakers simply adopted "Manakoora" as the name of a fictional island in Polynesia.