List of possible children posted by Forfarian on 13 Jun which I have updated in red to show children with parents William and Margaret who were registered in the correct area
John, 1874
Mary, 1875
Margaret Ann, 1875
John Dunnett, 1875
George, 1876
William, 1877 *** Registered in Buller District
William, 1877
Elizabeth, 1877
Margaret, 1879
Alexander Meanock, 1879
Peter, 1881 *** Registered in Buller District
Benjamina Jessie, 1882
James, 1883
Isabella, 1884 *** Registered in Buller District
William Alexander Procter, 1885
Amelia Florence, 1886
Elizabeth Anne, 1888 ** Registered in Buller District
James, 1890 ** Registered in Buller District
And one that got away!
Andrew Casey Henderson 1886 Registered Buller District
This 1886 birth is not on the NZ BDM site but, is found on Ancestry ?