Age given as 51 in 1901 census makes him born in 1850 but his Date of Birth in 1st Kilrea Presbyterian Church records is 1844. 

Death certificate gives him dying aged 84 (=Date of Birth of 1844) of "Cerebral Embolism 4 years Cardiac Failure", a farmer, of Lislea.  Thomas Gordon son Lislea informant.

Title : Mr Date of Death : 7 July 1928
Surname : Gordon Date of Grant : 7 January 1929
Forename : James Reseal Date : 
Registry : Londonderry Effects : Effects £109 10s 0d 
No Image 
Full Abstract :
Gordon James of Lislea county Londonderry farmer died 7 July 1928 Probate Londonderry 7 January to Thomas Hugh Boyd and Thomas Gordon farmers. Effects £109 10s.

Date of Birth from Public Record Office of Northern Ireland via Al Luce. (1901 census gives her as 32!! = Date of Birth of 1869 = first son, my grandfather, Tommy Gordon,  at age 15!!).  

Margaret Knox says Edna Peden remembers Jane Coulter and Edna was born in 1931.  So she must have died after this date.  But Janelle Stephenson says: "that her mother (Martha) was unable to attend her grannys (Jane Coulter) funeral as she was having a baby. She said that was Gordon so 1926."
Janelle was wrong, Edna was right.  Found Jane's death in the Civil Records Deaths Index at Derry FHC in the March Quarter of 1935.  Her age was given as 72.
Sue Coulter: "Janelle said that her grandmother Jane Coulter was buried at Kilrea Presbyterian Church, and she thinks there is a head stone."
 

I assume this is him:
name:    John Gordon
registration district:    Ballymoney
event type:    DEATHS
registration quarter and year:    Oct - Dec 1889
estimated birth year:    1882
age (at death):    7
volume number:    1
page number:    102
digital folder number:    4200677

Civil Birth Record
Name:    John Gordon    Date of Birth:    17-Aug-1882
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Male    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    James Gordon    Sponsor 2 /
Informant 2:

I am assuming this is him:
Registration number    Forename of deceased    Surname of deceased    Date of death    Age at death    Date of birth    Sex of deceased    Registration district    
D/1889/96/1008/7/370    John    Gordon    21st November 1889    7        Male    Coleraine(pre-1973 Q4)

Date of Birth of 24/02/1881 from Al Luce, using US WW1 Draft Registration card. Confirmed by 1901 census where he is 17.  I now have his Birth Record which gives his DoB as 21st February 1884 at Lislea, to Thomas Gordon, Farmer, and his wife, Jane Gordon, formerly Coulter; a Mary McKay "Aunt" from Lislea registered the birth and said she was present but she is his great aunt not his aunt.

Civil Birth Record
Name:    Thomas Gordon    Date of Birth:    21-Feb-1884
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Male    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    Mary McKay    Sponsor 2 /
Informant 2:

IFHF shows this child born to James Gordon and Jane Coulter:
Source    Surname    First Name    Year    County
Civil Birth    Gordon    John    1882    Co. Derry
Civil Birth    Gordon    Thomas    1884    Co. Derry
Civil Birth    Gordon    Hugh    1886    Co. Derry
Civil Birth    Gordon    Margaret Ann    1888    Co. Derry
Civil Birth    Gordon    Jane Elizabeth    1890    Co. Derry
Civil Birth    Gordon    Annie    1892    Co. Derry
Civil Birth    Gordon    Mary    1894    Co. Derry
Civil Birth    Gordon    Essie Amelia    1896    Co. Derry
Civil Birth    Gordon    Martha Ellen    1899    Co. Derry
Civil Birth    Gordon    Sarah Matilda    1899    Co. Derry
This shows that my grandfather, Tommy Gordon, had two brothers but both must have died which was why he had to return from New York to tend the family farm in 1920.

Title :     Mr     Date of Death :     24 September 1957
Surname :     Gordon     Date of Grant :     13 February 1958
Forename :     Thomas     Reseal Date :    
Registry :     Belfast     Effects :     Effects £2383 16s 8d
No Image
Full Abstract :
Gordon Thomas of Lislea Portglenone county Londonderry retired farmer died 24 September 1957 at Woodland Park Kilrea county Londonderry Administration Belfast 13 February to Margaret Adeline Turner married woman. Effects £2383 16s. 8d.

I assume this is him:
name:    Hugh Gordon
registration district:    Ballymoney
event type:    BIRTHS
registration quarter and year:    Apr - Jun 1886
volume number:    1
page number:    153
digital folder number:    4193975

I think this is Hugh:
name:    Hugh Gordon
registration district:    Ballymoney
event type:    DEATHS
registration quarter and year:    Apr - Jun 1887
estimated birth year:    1887
age (at death):    0
volume number:    1
page number:    113
digital folder number:    4200676

Civil Birth Record
Name:    Hugh Gordon    Date of Birth:    21-May-1886
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Male    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    Mary McKeag?    Sponsor 2 /
Informant 2:

I am assuming this is him.
D/1887/96/1008/7/46    Hugh    Gordon    29th March 1887    0        Male    Coleraine(pre-1973 Q4)

Age from 1901 census.

Civil Birth Record
Name:    Margaret Ann Gordon    Date of Birth:    14-Apr-1888
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Female    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    Mary McLeary?    Sponsor 2 /
Informant 2:

Date of Birth from 1901 census.  She gave her age as 29 in the 1920 census in New York, and 39 in the 1930 census in Detroit.

Civil Birth Record
Name:    Jane Elizabeth Gordon    Date of Birth:    30-Jul-1890
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Female    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Labourer    
Sponsor 1 /
Informant 1:    Mary McKay    Sponsor 2 /
Informant 2:    
Notes:
INFORMANT IS RECORDED AS BEING THE CHILD'S AUNT

Social Security Death Index about Elizabeth Gordon
Name:    Elizabeth Gordon    
SSN:    336-10-7429
Last Residence:    49043  Covert, Van Buren, Michigan, United States of America
Born:    12 Jun 1890
Died:    May 1973
State (Year) SSN issued:    Illinois (Before 1951)

This cannot be right as her name was Matthies by her death.

Date of Birth as per 1901 census.

Civil Birth Record
Name:    Annie Gordon    Date of Birth:    06-Jul-1892
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Female    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    Mary Laughlin    Sponsor 2 /
Informant 2:

Date of Birth from 1901 census - confirmed by Ellis Island Records record of entry to USA.

Civil Birth Record
Name:    Mary Gordon    Date of Birth:    06-Jun-1894
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Female    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    Mary Loughlin    Sponsor 2 /
Informant 2:

Ancestry.com:
Ireland, Civil Registration Births Index, 1864-1958 about Mary Gordon
Name:    Mary Gordon
Date of Registration:    Apr-May-Jun 1894
Registration district:    Ballymoney
Birth Country:    Ireland
Volume:    1
Page:    139
FHL Film Number:    101065

Date of Birth from 1901 census.

Civil Birth Record
Name:    Essie Amelia Gordon    Date of Birth:    03-May-1896
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Female    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    Jane Gordon    Sponsor 2

Appears to be a twin according to 1901 census return.

Civil Birth Record
Name:    Martha Ellen Gordon    Date of Birth:    15-Sep-1899
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Female    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    Jane Gordon    Sponsor 2 /
Informant 2:    
Notes:
TWIN OF SARAH MATILDA

In Armagh - data from Sue Coulter's A.com tree.

Appears to be a twin from the 1901 census return.

Civil Birth Record
Name:    Sarah Matilda Gordon    Date of Birth:    15-Sep-1899
         Registration Date:    1-Jan-0
Address:    Lislea    Parish/District:    KILREA
Gender:    Female    County    Co. Derry
Denomination:    Registrar District
Father:    James Gordon    Mother:    Jane Coulter
Occupation:    Farmer    
Sponsor 1 /
Informant 1:    Jane Gordon    Sponsor 2 /
Informant 2:    
Notes:
TWIN OF MARTHA ELLEN

Source: Sue Coulter