I think this is your FAHEY family in New Zealand -
From FamilySearch, NZ immigrants -
Arrived "Merope" Canterbury
FAHEY Patrick, 29 years (born ~ 1842), wife Bridget, daughter Mary.
Above their names is notation "Fitzgibbon Rolleston" Another notation to the left, which I am unable to transcribe.
Patrick FAHEY, late of Loburn d. 1904, and buried in plot with Mary FAHEY, died 1891, age 50. Mary is sister-in-law of E LLOYD, Halswell.
Press 31 Dec 1914 p4
https://paperspast.natlib.govt.nz/newspapers/CHP19141231.2.23.1?...Norah LLOYD, 79...Mary LLOYD 40.......running a brothel.....idle disorderly etc......
New Zealand Truth 2 Feb 1907 p6
https://paperspast.natlib.govt.nz/newspapers/NZTR19070202.2.48.1?....maintenance...paternity...William HAYES......child born to Mary LLOYD 16 Aug 1906.....Mary's mother is Norah LLOYD.....father is Emanuel LLOYD........Mary is 30 years old and has an older child.....
See FamilySearch for this -
The Estate of Bridget FITZGIBBON died intestate, 1887
Estate of Bridget FITZGIBBON, formerly the wife of Patrick FITZGIBBON of Loburn,
Executors Norah LLOYD wife of Emmanuel LLOYD of Papanui and Alfred Edward TUTTON..
...sale of her (Bridget's) farm at Rolleston......
Affidavit James WALLACE (image 37)...
.......from England "Tongariro" in company with Patrick FITZGIBBON and his wife Bridget FITZGIBBON....Bridget died 28 Nov 1887 and buried at sea
Statement Norah LLOYD (image 41).....Bridget went to Ireland......Bridget has surviving her, one brother and no more Patrick FAHEY of Loburn...three sisters...Ellen HAYES of Halswell, Mary FAHEY, spinster, and myself.....
Whereabouts of Patrick FITZGIBBON unknown.......
* Norah LLOYD signs with her mark.
When Patrick FAHEY arrived in NZ, 1871, he had sisters Ellen, Bridget and Norah living there. They had arrived as single women. Sister Mary arrived after Patrick...1871+...
BDM NZ marriage
1867/7372 FAHY Bridget m. FITZGIBBON Patrick
1868/6005 FAHEY AKA FARHEA Ellen m. HAYES William
1869/7317 FAY Norah Hannah m. LLOYD Emmanuel
BDM NZ birth
906/16105 LLOYD James Cyril parents Mary / -
1896/13487 LLOYD William Francis Harold Hayes parents Mary / -