Somewhere in Anthony Alpers' book "The World of the Polynesians" there is a translation of a short musical drama about Captain Cook's visit to Mangaia (?I think) written down by a missionary within living memory of the event. Text and sorta-stage-directions but no tunes, though.

There is also a tune commemorating Mai (or "Omai" as the Europeans called him), the Tahitian who came back with Cook to London.

  X:2
  T:Omai
  S:William Campbell: New and Favourite Country Dances, book 2
  N:Dundee, Wighton, 92520 H
  M:4/4
  L:1/8
  K:Dmin
  d>ed^c      Ddde       |fdcA                 FGEC           |\
  ded^c       Ddde       |fd     f/e/d/^c/     d2          d2:|
  fd a/b/a/g/ ec g/a/g/f/|de/f/ (g/f/).e/.d/ (^c/d/).e/.c/ A2 |\
  F>GFE       Ddde       |fd^cA                d2          D2:|