John's father was John Ings (1779-1858) .. When John emigrated to New Zealand he had added the name Daysh to the end of his name.
The children born in England appear to have the hyphenated name of Ings-Daysh but the children born in New Zealand have not.
In the 1841 census of Holts Hill, Wckham, Hampshire, England
John Ings - 33 - Agricultural labourer
Elizabeth Ings - 29
George Ings - 8
Elizabeth Ings - 7
Susan Ings - 6
Richmond Ings - 4
Mary Ings - 2
John Ings 4 months
In the 1851 census John Ings became John Ings Daysh

John, with his wife Elizabeth and the 1st 6 of their 15 children sailed from Gravesend on the 'Gertrude' leaving on the 19 June 1841, arriving at Port Nicholson (now Wellington) New Zealand on 30 Oct. 1841 - a journey of 134 days.
Gertrude Passenger List: http://tinyurl.com/2zkc535x

He married Elizabeth Clark on 9 Feb 1832 in St Nicholas Church, Wickham, Hampshire
Their 15 children
. (born Wickham) .
1832 - 1906 George Ings-Daysh
1833 - 1901 Elizabeth Mary 'Betsy' Ings-Daysh (+Southee +Rayner)
1835 - 1921 Susan Ings-Daysh (+Gaskin)
1837 - 1917 Richmond Ings-Daysh (+Cooper)
1839 - 1918 Mary Ann Ings (+Harris)
1840 - 1932 John Ings-Daysh (+Tannahill)
. (born Taita) .
1842 - 1919 Caroline Daysh (+Buck)
1844 - 1930 Sarah Daysh (+McEwen)
1846 - 1889 Esther Daysh (+Mabey +Russell)
1847 - 1920 Jane Daysh (+Swafford)
1851 - 1914 Eliza Ann 'Annie' Daysh (+Oxley)
1854 - 1940 Alfred Daysh (+Sage)
1856 - 1926 Emily Daysh (+Hollis)
1859 - 1936 Henry 'Harry' Daysh (+Davey +Rose)
1861 - 1888 Margaret Daysh (+McPhee)

Otago Witness, 21 Jan 1897
This district (says a Palmerston North paper) boasts of what probably no other part of the colony can - viz, five living generation of one family
At the head is Mr J. Daysh of Taratahi, who, although he is 92 years old, is still hale and hearty. He came out in the second or third boat of pioneer settlers in 1840
Mr John Rayner is his daughter and is 63 years of age. One of her daughters married a Mr George Gaskin, whose daughter again is the wife of Mr W. Knowles and their five-month-old son is a great-great-grandson to Mr Daysh. They are all enjoying good health

Evening Post, 3rd July 1900
The other day Mr Plimmer was the recipient of souvenirs on his attaining his 88th birthday, and looking equal to a few more years yet. Mr Daysh, a fellow-passenger with Mr Plimmer in the ship Gertrude, is still living in the Wairarapa, hale, hearty, and active, with an ever-green memory, after having reached the age of 98 (it was actually 95). Mr Daysh was for many years farming at the Taita before settling in the Wairarapa, and frequently visits Wellington to see his children, grand-child, and great-grand-children, assuring all inquiring friends that he intends to notch the century

He died aged 97, 32 years after Elizabeth.
Wairarapa News, 7 May 1902 Mr John Daysh, a very early settler in the Wairarapa, who arrived at Wellington in the ship Gertrude in 1841, died at the residence of his son-in-law, Mr John Rayner, (daughter Elizabeth) at Taratahi, this morning. Deceased was ninety-seven years of age.

A Family Tree .. http://tinyurl.com/2dkvx66j