Thinking laterally, local museums around Otago might have some record of the couple. The Lawrence Museum might not have much after 1880's, perhaps, but should be able to suggest other places to search:
Otago Museum
419 Great King Street, Dunedin
Central Stories Museum and Art Gallery
21 Centennial Avenue, ALEXANDRA
Lawrence Information Centre and Goldfields Museum
17 Ross Place, LAWRENCE
North Otago Museum
60 Thames Street, OAMARU
Lake Wanaka I-SITE Visitor Centre
WANAKA
Lakes District Museum
49 Buckingham Street, ARROWTOWN
South Otago Historical Society
1 Renfrew Street, BALCLUTHA
Visitors Information Centre
4 Clyde Street, BALCLUTHA
riley