Searching the BDM register using "Isabella" as the mother's name returned only one name

1904/20943 Beattie Alexander Matthew Mother: Isabella Father: Matthew

Using "Bella" as the mother's name was more successful:

1899/1429 Beattie, John McKenzie Mother: Bella Father: Matthew
1898/8272 Beattie, Marion Janet Mother: Bella Father: Matthew
1901/17208 Beattie, Jessie Wheliminea Mother: Bella Father: Matthew
1902/9232 Beattie, William Kenneth Mother: Bella Father: Matthew

It appears their youngest son died at the age of 3:

"BEATTIE--At Blenheim, on March 3rd, Matthew Alexander, youngest son of Mr and Mrs Matthew Beattie, Maxwell Road, aged three years and four months."

Marlborough Express, Volume XLII, Issue 52, 3 March 1908, Page 4.

1908/1469 Beattie Matthew Alexander 3Y

It appears one of the children was put in an institution:

"Before Mr F. O'B Loughnan, S.M., to-day, Matthew Beattie was charged with having failed to comply with an order for the payment of 5s a week for the maintenance of a child committed to an industrial institution. The amount of arrears was stated to be ?19 15s. Mr T. Scott-Smith appeared for the defendant, and explained that the father was unable to meet the liability imposed on him. Sergeant Hanson protested that the defendant had made no real attempt to satisfy the order. The defendant having given evidence, the case was adjourned for one month."

Marlborough Express, Volume XLVIII, Issue 157, 7 July 1914, Page 4

I also found a report of Matthew and Isabella's wedding:

"Marlborough Express, Volume XLII, Issue 52, 3 March 1908, Page 5

A pretty wedding was celebrated at St. Andrew's Church, Wellington by the Rev O. S. Ogg on Wednesday afternoon, the contracting parties being Mr Matthew Beattie and Miss Isabella McKenzie. The bride, who was given away by Mr John Robinson, was dressed in a lovely heliotrope tulle poplin dress with hat to match, and was attended by two bridesmaids, Miss Isabella Rees (in brown) and Miss Dora Tait, niece of the bride in blue velvet with white felt hat). The bride wore a handsome gold watch and chain and brooch, the gift of the bridegroom, and each bridesmaid also wore a gold brooch, the present of the bridegroom, Mr Len Dodson acted as best man. The wedding breakfast was provided by Mrs Tait, and about 80 or 90 guests were present, including a large sprinkling from Blenheim. The presents were both handsome and numerous, and included a marble clock and two dinner services, carvers, silver service, rings, etc. Mr and Mrs Beattie who are both well known m Marlborough, will have the best wishes of hosts of friends.

Marlborough Express, Volume XXXII, Issue 98, 29 April 1897, Page 2

1897/1281 Isabella McKenzie Matthew Beattie

Thank you BrightWings, I have found out that information in the past week, I'm really trying at the moment to ascertain whether or not the children of Matthew and Isabella had any children themselves. I obviously know that John Mckenzie did, he was my grandfather he came to Australia and changed his name. I have only recently discovered that he changed his name.