There are several journals that regularly publish articles on New Zealand archaeology. They have page links below.
But see also:
Papers often appear listed in academia.edu  It has a sign up requirement for readers - but it is free.
Academia.edu has various research interest groups but one with many papers is New Zealand Archaeology: 
Papers may also be uploaded here by researchers.
These are not listed separately below. They are annual publications that regularly include archaeological papers by museum staff or related researchers or by others on the museum's collections. Recent issues are available free on line.
Records of the Auckland Museum 
Tuhinga: Records of the Museum of New Zealand Te Papa Tongarewa 
Records of the Canterbury Museum 
Not all work appears in published journals. See Grey Literature for a guide to accessing this.
Academic Papers Notices
Recent academic papers are listed in a section in editions of Archaeology in New Zealand.
This category has only the following subcategory.