Original post doesn't actually ask for traditional songs per se -- so, going with the description of the singer's beautiful voice, she might want to look at songs such as 'How Can I Keep from Singing' (and maybe check for Annie Mayo Muir or Bok, Trickett and Muir on YouTube. And there's a great, gentle little song called 'The Garden Song/Inch by Inch' which would sit very nicely on the ukulele. Also, lots of tuneful and thoughtful songs by Pete Seeger.

And to follow on from Jack's indication of a strong Scottish background in New Zealand (if the mention of Maori language isn't just a happy circumstance), maybe start with some lyrical Scots chorus songs like 'Lassie wi the Yellow Coatie', 'Busk, Busk, Bonnie Lassie/Bonnie Glenshee', 'I'm a Poor Rovin' Lassie' etc. -- if these aren't as overdone as they are here.

And if the lady concerned really wants to dive deep into traditional, she might want to consider a version of 'The Cruel Mother' collected by Robert Burns and usually known as 'Fine Flowers in the Valley' -- all the essence of a big, tragic story but delivered with a haunting tune and refrain.

Hope this opens up some new ideas for the original poster.