You're probably going to have more chance of tracking them - and especially her - in Ireland with more data from New Zealand, if you can find it (or know it already).
Their 1874 NZ Marriage: indexed as Cornelius CROWLEY & Catherine KELLY:
Have you the record of this marriage?
Parents names? Ages? Occupations? Witness? Bachelor, Spinster?
Their Deaths in NZ 1904 & 1922:
Have you obtained the Death registration Printout for their deaths (more info than the certificate)?
Parents Names? Length of time in NZ Funeral Director's name?
If you don't have any of the above extra information, then if you can establish who buried them, chances are the funeral director may still be in business and MAY hold offline (card) records on their funeral/burial. Very often, parents names, siblings names, childrens names are on these cards if they exist. A respectful call to the director can have results. May have more luck with Catherine (more recent) - and she's the one with the very common name you're going to have trouble going further with, without more details on her.
I note they had a son named Cornelius:
Referenced on death index as: Cornelius Michael Stowers CROWLEY
Referenced on cenotaph WW1 as: Cornelius Michael Storers CROWLEY
'Stowers' seems more likely than 'Stores'.
For our Reference:
Cornelius Stores CROWLEY
Died 1904, Reefton Otago, NZ age 59.
Buried 31 May 1904, in Old Reefton Cemetery, Plot 268
Burial Record online: says born Cork Ireland
Catherine CROWLEY
Died 1922, Reefton, Otago, NZ, age 72.
Buried 6 Sep 1922, in Old Reefton Cemetery, Plot 268
Burial Record online: says born Ireland
She's referenced as 'Kate' on some of her son's WW1 records.
The Cemetery online:
http://bullerdc.govt.nz/cemeteries/Their Gravestone:
https://billiongraves.com/grave/Cornelius-S-Crowley/11214558#
Stowers Crowley
Here's two more men with that middlename / surname combination - and could well be brothers:
ONE: Robert Stowers CROWLEYB abt 1849, Cork, Ireland
D 1927, San Francisco, USA
1880 Directory : 856½ Harrison, San Francisco
California Voters RegisterAppears in various with middle name transcribed as Stoars, Stoers, Stowers, Storers, Stores
Naturalisation 1877Naturalised 8 Oct 1877, Boston MA
Oath of Allegience, 9 Oct 1877 - Robert S CROWLEY, Clerk.
Petition of Robert S CROWLEY - Age 28 years, Clerk of Boston MA.,. Born County Cork, Ireland on 28 Apr 1849. Arrived New York July 1863 as a minor aged under age 18.
1880 Census: 856½ Harrison, San Francisco
Robt CROWLEY 27, b Ireland, single, Clerk in Store.
1900 Census: San Francisco
Robert S CROWLEY 48, married1, b April , Ireland, imm 1876, a Salesman
Wife is Nellie M.
1910 Census: San Francisco
Robert S CROWLEY 57, married 1 (26 yrs), b Ireland, imm 1880, Na. a Clerk
Wife is Mary Ellen
Robert S CROWLEY died 2 June 1927, San Francisco, age 77 years.
They had a son, Robert Stowers CROWLEY Jnr
Born 19 Jul 1894
Died 9 Mar 1954, age 59, single
Father: Robert S CROWLEY, b Ireland
Mother: Nellie M CURLEY, b San Francisco
Buried Holy Cross Cemetery
TWO:George Stowers CROWLEYB abt 1858, Ireland
D 1906, Bantry, Cork, Ireland
http://www.from-ireland.net/full-gravestone-transcriptions/bantry-cork/Bantry Gravestone Transcriptions, Bantry. Co. CorkCrowley: Sacred to the memory / of / George Stowers Crowley / Alderman / died 1st Jan 1906 aged 48 years / R.I.P. / this monument was erected / by his colleagues of the / Cork Corporation / the west ward branch of the U.I. league / and his many admirers / as a tribute of respect to one who was / a true Irishman and a sincere friend / ..................(more)
http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=149202579Cheers
AMBLY