Hi David,
Do you have the marriage certificate? It will almost certainly hold the names of both of her parents, and the father's occupation. Otherwise, a death certificate will have the same information, plus how long she's resided in NZ, where she was married + to whom (even though you know that part already). They don't mail out physical copies any more, so it's an even faster turnaround because they fire you an email with the pdf file. Absolutely worth it for the information that can be gleaned from it.
Otherwise, was just looking on Ancestry and there seem to be a couple of Sarah Ann Berryman's floating around Cornwall who were born between 1858 and 1863.
1861 Census
Name: Sarah Berriman
Age: 2
Estimated Birth Year: abt 1859
Relation: Daughter
Father's Name: Samuel Berriman
Mother's Name: Jane Berriman
Gender: Female
Where born: Camborne, Cornwall, England
Civil Parish: Camborne
Ecclesiastical parish: St John
County/Island: Cornwall
Country: England
Samuel Berriman 41
Jane Berriman 41
Susan Jane Berriman 18
Alice Berriman 16
Samuel Berriman 13
Henry Berriman 12
George Berriman 10
Emma Berriman 7
Emily Berriman 6
Thomas Berriman 4
Sarah Berriman 2
1871 Census
Name: Sarah Berryman
Age: 12
Estimated Birth Year: abt 1859
Relation: Daughter
Mother's Name: Jane Berryman
Gender: Female
Where born: Camborne, Cornwall, England
Civil Parish: Camborne
Ecclesiastical parish: St Martin
Town: Killivose
County/Island: Cornwall
Country: England
Jane Berryman 48
Elizabeth E Berryman 23
Henry Berryman 22
Emma Berryman 18
Emily Berryman 16
Sarah Berryman 12
Thomas Berryman 14
Joseph Hart 28
Alice Hart 26
H A Hart 10 Months
1881 Census:
Name: Sarah Berriman
Age: 22
Estimated Birth Year: abt 1859
Relationship to Head: Daughter
Mother: Jane Berriman
Gender: Female
Where born: Camborne, Cornwall, England
Civil Parish: Camborne
County/Island: Cornwall
Country: England
Jane Berriman 58
Emily Tippet 25
Sarah Berriman 22
Arthur Hart 11
Joseph Hart 10
These three look like they belong together, but it won't be this lot, as the NZ BDM records say she was in NZ getting married before the 1881 census took place.
Otherwise there is this Sarah, which actually looks promising, as she does not appear on the 1881 census which matches the other family members;
1861 Census:
Name: Sarah Ann Berryman
Age: 2
Estimated Birth Year: abt 1859
Relation: Daughter
Father's Name: James Berryman
Mother's Name: Jane Berryman
Gender: Female
Where born: Ludgvan, Cornwall, England
Civil Parish: Ludgvan
County/Island: Cornwall
Country: England
James Berryman 26
Jane Berryman 28
James Berryman 8
Elizabeth Jane Berryman 7
Mary Berryman 5
Sarah Ann Berryman 2
1871 Census:
Name: Sarah Berriman
Age: 12
Estimated Birth Year: abt 1859
Relation: Daughter
Father's Name: James Berriman
Mother's Name: Jane Berriman
Gender: Female
Where born: St Hilary, Cornwall, England
Civil Parish: Marazion
County/Island: Cornwall
Country: England
James Berriman 38
Jane Berriman 30
James Berriman 19
Mary Berriman 15
Jane Berriman 16
Sarah Berriman 12
John Berriman 11
Susan Berriman 7
Ellen Berriman 2
1881 Census:
Name: James Berriman
Age: 48
Estimated Birth Year: abt 1833
Relationship to Head: Head
Spouse: Jane Berriman
Gender: Male
Where born: St Hilary, Cornwall, England
Civil Parish: Madron
County/Island: Cornwall
Country: England
James Berriman 48
Jane Berriman 46
Jane Berriman 26
Mary Berriman 24
John Berriman 22
Susan Berriman 17
William Berriman 9
Hope this helps, do you have an Ancestry subscription? If not, I'm more than happy to look things up, it gives me a break from banging my head over my own stuff

Cheery
Georgia