Hopefully this will get you on your way:
Joseph Price was the son of Nelson Colonist, Thomas Price. It appears that Thomas Price arrived in New Zealand prior to 7 Oct 1843. Nelson Examiner and New Zealand Chronicle, 7 October 1843, Page 330. Arrived. 4th, brigantine Star of China, 112, Ward, from Wellington; general cargo. Passengers, Mr. Perry, Mr. Price, Mr. Dorter, and two in the steerage. (The Star of China came either from or via Sydney, AU) (Also, a Millard, possibly the father of Joseph's wife, was a Nelson Colonist)
Birth reg for Joseph: 1848/374 Price Joseph
By 1852 Thomas Price aquired a land grant at Waimea South. In 1862 he starts appearing in newspapers, along with his sons Thomas Jr. and Joseph. In a 1864 news article Thomas states that he is a servant to Captain Blundell and he owns land in Waimea West.
PapersPast has other articles about the marriages of his children, deaths, etc. I suggest you enter these exact search terms "Thomas Price" "Waimea West" with the parens around them, and choose Articles as the content type.Then do a search changing the name to "Joseph Price"
Thomas Price was married to Mary Ann, who died 14 Sep 1870, age 59 at Waimea West. (gives a birth year of about 1811)
Thomas Price died 15 Aug 1886 at Waimea West, age 83 years (gives a birth year of about 1803). He and Mary Ann were buried at St Michaels Cemetery (St Michaels Anglican Church), Waimea West
