|Ranapia Mokena's Miners' Right taken out 23rd August 1867|
There is a wealth of information on mining at the Auckland Archives, that stretches up to the 1970s.
There are card indexes available in the index room adjacent to the main reading room - that have reference details for each miner and mines they were associated with. Then in Miners Index Books for instance, there are alphabetically listed names of mine applications by surname. The one below is for 1965.
December 2014 update:
Since writing this, The Treasury at Thames have been obtaining copies of many miner's rights
Also remember you can check Kae's Goldminers Index for the years: 1867 - 1872