Ingrid,
I can’t see Nathaniel and Rose’s marriage in the statutory registers so it looks as though they married before April 1845, in which case you would need to check church records. Have you any idea what denomination Rose was? (Tradition was to marry in the bride’s church).
I see a William Graham in Creevamoy in Griffiths for 1862. He had a 20 acre farm there. A relative perhaps? Only Graham in Creevamoy in 1901 was this lady, who was Presbyterian:
http://www.census.nationalarchives.ie/pages/1901/Antrim/Broughshane/Crevamoy/927831/
No Grahams in Drumleckney in Griffiths or the 1901 census.
There were Gordons though, again Presbyterian:
http://www.census.nationalarchives.ie/pages/1901/Antrim/Broughshane/Drumlickney/927857/
Griffiths has James, William & Thomas Gordon in 1862 in Drumleckney.
You can follow through to see the change of occupants of those farms using the revaluation records on the PRONI website.
Both townlands are quite small so if this is where the family originated, then chances are these are relatives.
Probate abstract:
The Will of William Graham late of Crevamoy County Antrim Farmer deceased who died in the month of September 1876 at same place was proved at Belfast by the oaths of John Fleck of Drummack and Adam Turtle of Drumleckney both in (Broughshane) same County Farmers the Executors.
Chances are the couple attended either Buckna Presbyterian or 1st Broughshane. Buckna’s baptisms start in 1836 (though there is an index to baptisms for 1828 – 1836), and marriages in 1830 only, and then 1845 onwards. (Earlier records lost). 1st Broughshane has baptisms from 1827 – 1832 and then 1836 onwards, plus marriages 1845 onwards. Again earlier records are lost. (Copies of the surviving records are in paper format in PRONI).
The tithe applotment records for 1825 list William Graham as the only Graham in Creevamoy, so that’s a tenuous hint he could be Nat’s father. In Drumleckney there were 4 Gordon properties, held by Patrick, James, Thomas senior & Thomas junior.
http://www.irishgenealogyhub.com/antrim/tithe-applotments/skerry-parish.php#.WAgy8BR9eg0
The Gordons may have used Racavan burial ground. Found this inscription on the Braid site:
Erected by John Gordon, in memory of his Uncle, Thomas Gordon, of Drumlicknay, who died 16th Jan, 1831, aged 88 yrs.
Bur also found this one in 1st Broughshane:
Erected by Agnes Gordon, Drumlickney in memory of her husband Nathaniel Gordon who died 30th June 18084 aged 62 years Also their son Nathaniel who died in infancy
Plenty of other Gordon & Graham headstones in that area but not all give the townlands so difficult to say whether they relate to your family:
http://thebraid.com/genealogy.aspx