This Wiki article
Pokarekare Ana claims that 'Pokarekare Ana is a traditional New Zealand love song, probably communally composed about the time World War I began in 1914. The song is written in Maori and has been translated into English.

'East Coast Maori songwriter Paraire Tomoana, who polished up the song in 1917 and published the words in 1921, wrote that "it emanated from the North of Auckland" and was popularised by Maori soldiers who were training near Auckland before embarking for the war in Europe.[1]

'There have been numerous claims and counterclaims regarding authorship over the years. Although the matter has never been definitively settled, guardianship of the words and music is held by the family (descendants) of Paraire Tomoana.'

And that: 'The melody of "Pokarekare Ana" was used for an Irish hymn to the Blessed Virgin: "A Mhuire Mháthair, sé seo mo ghuí".'

Just throwing that into the discussion. The wiki article itself doesn't really supply any evidence for when and where the tune was originally composed but the article referred to in this footnote might shed some factual light, if someone can access it: 1. Allan Thomas. ""Pokarekare": An Overlooked New Zealand Folksong? . Journal of Folklore Research. Indiana University Press (Vol. 44, No. 2/3 (May – December, 2007)): 227–237. JSTOR 40206952.

Is it possible that the lyrics of A Mhuire Mháthair were written in the 1700's - as claimed above - but that the words were then fitted to the melody of "Pokarekare Ana" in the 1900's?

I know nothing!! But this thread raises some interesting questions.