there are 14 counties with 123 Cogan head of house listed in Griffiths valuation this reduces to 6 counties with just 12 or 13 strong clues if Patrick/Patk, if the father was alive at the time of record taking which varies but all are before 1864 and he was head of household.
to date each line you will need to search the entry in
http://www.askaboutireland.ie/griffith-valuation/ Cogan Patk. Aghalion Castlerahan Cavan eg 1856
Cogan Patrick Aghalion Castlerahan Cavan eg 1856
Cogan Patrick Cornakelly Castlerahan Cavan
Cogan Patrick Quarry Road St. Nicholas Cork
Cogan Patrick Owen George's Street, Great, North St. Georges Dublin eg 1854
Cogan Patrick Collector's Lane Aglish Mayo eg 1857
Cogan Patrick Knockthomas Aglish Mayo eg 1857
Cogan Patrick Newantrim Aglish Mayo eg 1857
Cogan Patrick Sarnaght Aglish Mayo eg 1857
Cogan Patrick Cruicetown Cruicetown Meath eg 1857
Cogan Patrick Moat Killeagh Meath
Cogan Patrick Derreentunny Kilbryan Roscommon eg 1858
Cogan Patrick Owen Lung Castlemore Roscommon eg 1858
I tried searching quickly for Patrick and Ellen Cogan unsuccessfully on
https://churchrecords.irishgenealogy.ie/churchrecords/ i thought i had an 1851b for Ellen but wrong father unless the fahthers name was written down wrongly.
https://www.ancestryireland.com/I noticed Goggin was often found as a spelling variant, but still no luck
lets hope others will jump forward and help you get the connection