They used NZ jade (greenstone) if high ranking or native hardwoods, which are extremely solid. Made using stone adzes and stone hammers. Extremely effective weapons for their type of warfare prior to arrival of muskets.
I'm not a historian, and not Māori, but I did grow up in New Zealand.
I remember learning about three common weapons: patu (a club); mere (like a small club with a sharpish edge), and taiaha (a staff/long club).
Patu and mere were often made from various kinds of stone besides pounamu (jade), which was a valuable and high-status material. Other materials used included wood and whalebone.
Taiaha were made from wood, or sometimes whalebone.