Ohio Families

His 1900 census said he was born in September 1849.
Henry's death record said he was born August 25, 1849.
His son Henry's death record said that Henry (Sr) was born in County Down.
The Kilkeel Parish Baptism register has a baptism record for Henry, son of John and Catherine Rourke on August 27, 1848.
Either his death record or the baptism record is in error, likely the death record.

Kilkeel Parish Register, at nli.ie
August 27, 1848
Henry [son] of John Rourke and Catherine Rou
sponsors: Thomas Rourke and Margaret Cunningham

I found three Henry O'Rourke arrivals at New York in this time period, they are listed below.

None are in 1870, when his daughter Selina said he arrived, or in 1871, when his census information said he arrived. The one on September 16, 1872, matches Henry's year of birth the closest. The one on April 28, 1873, does not give him much time to marry Selina (Sloan) Sands and have a child by February 12, 1874. None of these three dates give him much time to make the acquaintance of Selina, but it's possible they knew each other in Ireland and the marriage was agreed upon before he arrived.

There is no evidence he was a miner; if he was, wouldn't he have gone farther west, e.g., Montana? If not, that would eliminate the first and third dates below.

arrived August 6, 1872, SS City of New York, from Liverpool and Queenstown
Henry O'Rourke, 26, miner, Ireland

SS Baltic, from Liverpool and Queenstown
arrived September 16, 1872
Henry O'Rourke, 22, laborer, Ireland

28 April 1873, SS City of Paris
Henry Rork, 22, a miner, Ireland

1880 Census, Cleveland
June 10, 1880
at 153 Alabama [became 1660 East 26th]
Henry O'Rourke, 30, born in Ireland, works at railroad roundhouse
Celina O'Rourke, 30, born in Ireland
Mary O'Rourke, 9
John H O'Rourke, 6
Francis J O'Rourke, 5
Margaret O'Rourke, 2
Annie O'Rourke, 4m [born January 1880]

all children born in Ohio

Petition for Naturalization
Probate Court, Cuyahoga County, Ohio
October 9, 1880
signed Henry Rourke
witness: B Flanigan, of 145 Alabama

certificate of citizenship issued.

1900 Census, Cleveland
June 4, 1900
owns the house, free of mortage, at 153 Alabama [became 1660 East 26th]

Henry O'Rourke, 50, born September 1849, married 27 years, born in Ireland, parents also, arrived 1859, naturalized, railroad foreman, roundhouse
Selina O'Rourke, 50, born November 1849, married 27 years, 10 children, 7 alive, born in Ireland, parents also, arrived 1859
Henry J O'Rourke, 26, born February 1874, railroad bill clerk
Francis J O'Rourke, 25, born May 1875, railroad foreman, roundhouse
Margaret A O'Rourke, 23, born February 1877, school teacher
Anna E O'Rourke, 20, born January 1880, at school
William T O'Rourke, 19, born February 1881, machinist's apprentice
Selina O'Rourke, 15, born July 1884

all children born in Ohio

1910 Census
April 21, 1910
owns the home free of mortgage at 1660 East 26th

Henry O'Rourke, 59, married 1x, for 39 years, born in Ireland, parents also, arrived 1871, naturalized, dispatcher, steam railroad
Salina O'Rourke, 60, married 1x, for 39 years, 7 children, 7 alive, , born in Ireland, parents also, arrived 1871
Mary O'Rourke, 33, no occupation
Margaret O'Rourke, 30, teacher public schools
William O'Rourke, 27, machinist, steam railroad
Salina V O'Rourke, 24, stenographer, brokerage company

all children single, born in Ohio

This information comes from the index records of naturalized citizens which began being kept in 1912, I think. Henry's information below was recorded in 1919. He was actually naturalized on Oct 9, 1880.
Naturalization Index Card Record
date of card September 11, 1919
office # 43999
Henry O'Rourke
present address: 1700 East 82nd, ward 20
native of Ireland
naturalized October 11, 1880, Probate Court, Cleveland, Cuyahoga County
volume 13, page 565
age when naturalized: 31
age when recorded: 70
signed Henry O'Rourke
in county, state, and country 49 years

1920 Census
January 7, 1920
owns the home free of mortgage at 1700 East 82nd

Henry O'Rourke, 70, born in Ireland, parents also, arrived 1870, naturalized 1876, no occupation
Salina O'Rourke, 70, born in Ireland, parents also, arrived 1870, naturalized 1876
Margaret O'Rourke, 35, born in Ohio, teacher public school
Salina O'Rourke, 30, born in Ohio, stenographer, Catholic Charity?
William O'Rourke, 37, born in Ohio, machinist, railroad company
Minnie O'Rourke, 45, born in Ohio, no occupation

1930 Census
April 8, 1930
owns the home at 1700 East 82nd, owns a radio

Henry O'Rourke, 80, first married at 20, born in North Ireland, parents also, arrived 1870, naturalized, no occupation
Selina O'Rourke, 80, first married at 20, born in North Ireland, parents also, arrived 1870, naturalized
Mary O'Rourke, 57, no occupation
Margaret O'Rourke, 50, teacher, public school
William T O'Rourke, 47, machinist, steam railway
Selina B O'Rourke, 45, stenographer, street railway

all children single, born in Ohio

Certificate of Death, #21808
April 15, 1930
Henry O'Rourke
at his residence, 1700 E 82nd, Cleveland
white, male, married, retired
born August 25, 1849, Ireland
age 80y 7m 20d
wife: Selina
father: John O'Rourke, born in Ireland
mother: Catherine O'Rourke, born in Ireland (ok)
cause: artero sclerosis
contributory cause: heart failure
buried: Calvary, April 18, 1930
informant: William J O'Rourke, of 1700 East 82nd

Name: O'Rourke, Henry
Date: Apr 16 1930
Source: unknown, Reel #62
Notes: O'Rourke: Henry, beloved husband of Selina, father of Mary T., Henry J., Frank J., William T., Margaret, Mrs. C. L. Coreoran and Selina, Tuesday, April 15 1930, at his residence, 1700 E. 82d Street. Funeral Friday, April 18 from St. Agnes' Church at 10 a. m.