Some sources of funding for graduate living costs in New Zealand are linked to below:
(1) University scholarships are automatic for students with a GPA 8.0 (~A to A+ average, first class). If your degree is not from a New Zealand university you can calculate your Grade Point Equivalent (GPE) using this online calculater.
(2) There is also the NZIDRS scheme
(3) NZ Ministry of Foreign Affairs and Trade (MFAT) scholarships to students from some Asian and Pacific countries,
In some cases, students can get grants from their home country.
Fees are same for national and international students for a PhD, but much higher for an overseas MSc student. Check university for latest tuition fees.
Once accepted, the university provides reasonable funds for research costs for MSc and PhD students. There are several schemes for other small research funding grants for students but typically NZ$2,000. In addition, there are modest national grants aimed at community and school groups which may be able to support some graduate work.
Marine conservation funding sources are listed on Whalefish. The New Zealand Marine Sciences Society also provides small, once-off grants for research and travel to your first international conference.
Auckland is a relatively expensive city so earning enough on part-time work to also do full-time graduate studies is not really possible. There is information on living costs on this university webpage and in this book, including regarding rent for accommodation.