This site has more details regarding their children and Margaret Frew's family http://www.geni.com/people/Margaret-Frew/6000000025594783764
Margaret Frew married Alexander Campbell 1891/207
Alexander Campbell died aged 66 years old 1925/4726
Born c 1859
Margaret Frew born East Taieri, Otago, New Zealand 14 July 1861 died 16 April 1934 Invercargill, New Zealand
So it would be good to get the marriage cert to obtain Alexander's parents names and possibly where he originated from.
Sadly the Headstone/cemetery record doesn't give any helpful hints either. Only the date of death for Alexander and Margaret.
I still think the marriage cert is the way as it is late enough to supply both his parent's names and the birth location for Alexander. With that you can then hope that he wasn't born in New Zealand.
A 1859 birth certificate is only going to give you his parents names and then you would need some of his children's birth certs to find out where he originated from.
Well, Ross seems to think Alexander was born in New Zealand. If the 1859 date is correct the birth is likely 1859/9101 Alexander Campbell Parents Margaret and Malcolm.
Here's the marriage notice of Alexander and Margaret Frew: http://paperspast.natlib.govt.nz/cgi-bin/paperspast?a=d&cl=search&d=OW18910430.2.92&srpos=3&e=-------100--1----0alexander+campbell+margaret+frew--
It says Alexander is the the eldest son of Malcolm of Blueskin. Malcolm is deceased by 1891.
A sister of Alexander appears to be Margaret Lochhead Campbell. In her marriage notice to William McIntosh her father is listed as Malcolm Campbell of Blueskin. http://paperspast.natlib.govt.nz/cgi-bin/paperspast?a=d&cl=search&d=OW18970513.2.97&srpos=3&e=-------100--1----0malcolm+campbell+blueskin--
Margaret Lochhead Campbells parents were Malcolm and Margaret (NZBDM: 1867/28832) which would indicate the 1859 Alexander mentioned by Simon is correct. Also Alexander would be the eldest son of Malcolm and Margaret, with his siblings being: John(1861/11039), Malcolm(1863/16368), William(1865/18300) and Margaret.
The only Malcolm Campbell to die before 1891 in New Zealand from a search at bdmhistoricalrecords.dia.govt.nz died in 1869 aged 35(1869/9626).