Some more, up to 1865:

Gloucester
Ship: 591 tons
Sailed London September 14th 1858 - arrived Port Chalmers December 26th 1858
Dempster, Mr A & Mrs & Child

Pladda
982 tons
Arrived Port Chalmers 1860
Dempster, George, and wife
Births
On the 26th May, Mrs George Dempster of a son

Storm Cloud
797 tons
Sailed Glasgow, May 3 1861 - arrived July 30, 1861
Dempster, William

Pladda
982 tons
Sailed Glasgow, Arrived Port Chalmers September 7 1861
Dempster, David

Jessie Gilbert
634 Tons
Sailed Gravesend 6th January 1865 - arrived Dunedin (via Bluff) June 4th 1865
Dempster, Ann, aged 18 months
(This child's parents are not recorded on the passenger list).