Some of the jewelery shops in Nelson / Greymouth would be able to do that for you.
You won’t want to use 24k pure gold - as they wear thin, unless she keeps it in a box most of the time. So you’ll only need 18k. A ring will probably weigh about 4g, which means you only need about 4g of gold 
Let me tell you about maths. Due to impurities get 4 grams of gold, at the end you should get about 3 grams net. The jeweler will add 1 gram of copper.
You’re in a good area.