An authoritative Danish language course, which is supported by the Danish Ministry of Integration, is now available on the worldwide web. You can download a description of what they offer here (.pdf, 150Kb) or you can visit their website at http://www.danskabc.dk.
For more information about Danish course available on-line, please go to:
A Danish Language course is also available on a CD from the TradeMe website. Just search for Danish language to find it. The CD costs $16.95 and gives a very good introduction to the Danish language (and the 15 others on the CD).
The Danish Consulates in Auckland, Wellington and Christchurch may also be able to refer you to a local Danish person who may be willing to offer instruction in the Danish language.