According to the ship list he (& his children) were born in Queen's County (aka County Laois), about an hour (today) from Dublin.

William's first wife, Jane Macquire Lingard was born in Warrington, Lancashire. They married in 1856 in Warrington, Lancashire
they had 10 children
. born Warrington .
1857 - 1859 Ann Grinlinton (age 2 in Warrington)
1859 - 1945 Emma Grinlinton (+Davies)
1860 - 1909 Robert Eldon Grinlinton (+Sedcole)
1862 - Mary Jane Grinlinton
1854 - 1871 James William Grinlinton
1866 - 1870 Margaret Elizabeth Grinlinton (age 4 in Yorkshire)
. born Easington, Yorkshire .
1868 -1942 William Lingard Grinlinton
1870 - 1941 Harry Gregg Grinlinton (+Farmer, died Sydney)
1872 - 1873 Thomas Roden Grinlinton (age 1 in Yorkshire)
1873 - 1935 Ernest Roden Grinlinton (+Palmer)

William & Jane, with their 6 remaining children emigrated to NZ on the Winchester. They departed from London 3 May 1874, arriving in Napier 27 July 1874 among the 430 other passengers .. https://tinyurl.com/ydcdecpp

Jane died 29 Aug 1883 and buried in Napier
William next married Matilda Jemima Irwin (nee Armstrong 1848-1901) on 18 March 1884
they had 3 children
1885 - 1917 Irwin Goodwin Grinlinton (KIA Belgium)
1887 - 1960 Louisa Collier Grinlinton (+Wilson)
1888 - 1950 Vesey Gore Grinlinton

Woodville Examiner, 23 Nov 1914
GRINLINTON - At the residence of his son, William, at Pahiatua, on Monday 23rd November, William Nassau Grinlinton, late of Woodville and Napier; aged 84 years

Woodville Examiner, 23 Nov 1914
Obituary William Nassau Grinlinton
We regret to record the death of Mr W. N. Grinlinton, which took place at the residence of his son, Mr W. Grinlinton in Pahiatua, at half-past six this morning.
Mr Grinlinton was an old resident of the Dominion, having come to it forty years ago, settling in Napier at his business as a tailor. While he was there his son Robert came to Woodville and started business here in the early days and subsequently when Mr Grinlinton senior, retired from business he came to Woodville and resided with his son and his daughter, Mrs C. Davies. For a long time past he has been in very feeble health and his demise was not unexpected and must have been a release from much painful suffering.
For all his years, Mr Grinlinton was extremely interested in gardening, having been a constant exhibitor at the Flower Show till his strength for the work failed him and also in general questions. In politics he always took a keen interest and, curiously enough, it was on the opposite side to that taken by his sons here.
A man of kindly nature, he was much liked by those who met him and he had the respect of all. He leaves a large family, all grown up. It includes Mrs Davies and Messrs William, Ernest and Harry Grinlinton, Miss C. Grinlinton and Mr V. Grinlinton and there is a large number of grandchildren as well.
The friends of the late William. N. Grinlinton are respectfully invited to attend his Funeral which will leave the residence of Mrs R. E. Grinlinton, Ross Street, at 2.30 o'clock on Wednesday, 25th instant, for the Woodville Cemetery. - Ernest Grinlinton, Undertaker.

NOTES On son Irwin Goodwin Grinlinton, from above site ..
Irwin Goodwin Grinlinton was born in 1885 in Napier, Hawkes Bay, New Zealand. His parents were William Nassau Grinlinton and Matilda Jemima Irwin (nee Armstrong) who married in 1884 in NZ.
He had two and a half years previous service with the Senior Cadets in Napier, NZ before he enlisted in Randwick, Sydney NSW on 22nd August, 1914 with the Australian Army and embarked with the 2nd Australian Infantry Battalion on 18th October 1914 on the ship HMAT Suffolk.
Irwin was Killed in Action by an exploding shell on 6th November, 1917 in Belgium and first buried near where he fell & later re-interred in the Tyne Cot Cemetery in Belgium - his name is memorialised on the Australian War Memorial. He received a Distinguished Conduct Medal (DCM) for conspicuous gallantry & devotion to duty. He led his platoon with great dash, dislodged the enemy from a strong point and captured a machine gun. He was also awarded the 1914-15 Star, British War medal & the Victory Medal.
Irwin's brother Vesey Gore Grinlinton also served in WW1 as a Trooper in the NZ Army (Service No. 36267) with the 20th Reinforcements Mounted Rifles Brigade, Mounted Wireless section, 6th Troop - New Zealand Expeditionary Force. He survived the war and died on 6th July, 1950 in NZ and is buried in Pukekohe Public Cemetery