Tullamore Parish Records:
RC baptisms from 1819-1899 and marriages 1801-1899
Church of Ireland Tullamore(Kilbride) baptisms 1805-1899 marriages 1814-1899www.rootsireland.ie
He would of been at least 20-25 for marriage or 1801-1806. You might get lucky.
The earliest census substitute for Ireland is the Tithe Applotments 1823-1837www.genealogy.nationalarchives.ie
Joseph Coughlan 1827 Kings/Offaly but Parish Eglish.
There is a James, Parish Kilbride, Townland Erry also Killoughy is a
Farrell, Edward, Daniel and Mark all very unusual first names for the times.www.askaboutireland.ie
Griffith Valuation 1851 (census substitute) also has place name descriptions. It describes Tullamore as a Town, a townland in the Parish of Kilbride, and it is also a Poor Law Union, whose administrive area would cover 12 miles, the following Parishes are in the Tullamore Union:
Killaderry, Killough, Kilbride, Kilcumreragh, Kilmanaghan, Rahan, Geashill.
The names of Coughlan's with their own leases are Edward, James, Thomas, Polly, Patrick, Martin, Mary, Brien, John, Esther
are any of these common in your family.
The only real way to prove relationships are the parish registers and going through them yourself. However, just the fact they were in the same Parish makes it very likely. www.igp-web.com
+ county a good resource depending on the county.