I can't see a New Zealand Birth registration for Honoria (or var.) HORAN 
(Maybe though surname has been miss-spelled ? ) Will look again.
The following are the children registered to Sarah and Owen HORAN (who resided in Christchurch).
1883 - HORAN - Mary Ellen
[possibly the Mary Helena HORAN on e/rolls? ]1888 - HORAN - William John
1893 - HORAN - Euguent [sic] Aloysius
1899 - HORAN - Eileen Josephine
Parents: Sarah and Owen
also ...
1885 - HOREN - Norah
Parents: Sarah and Owen
1896 - HORAN - May Philomena
Parents: Jane (probably a transcription error ?) and Owen HORAN
[Can confirm that this May Philomena HORAN is on e/rolls at Christchurch at various times living with parents Sarah and Owen and with brother Eugene. ] -------
Probable NZ Marriage of parents ?
Owen HORAN - Sarah CUNNINGHAM -- 1882 [Will have another look at the Roman Catholic baptisms for Canterbury area to see if I can spot Honoria. ]
~ Lu
Highlighted in blue are additions to earlier post .