If Catherine’s father, Archibald, was a shoemaker, and you allow for the mangled spelling, this could be the family.
1841 Market St Greenock West
Archibald Kelly / 42 / Shoemaker
Katrine Kelly / 34
Katrine Kelly / 12
William Kelly / 2
All born Renfrewshire
1850 Patrick MIGHAN & Catherine Kelly, married Greenock Old or West
1851 Market St, Greenock West
Archd Kelly / 50 / shoemaker / Ireland
Elizabeth Kelly / 47 / Greenock
Patrick Mccann / 24 / Son in Law / Dock Labourer / Ireland
Catherine Mccann /21 / Dau / Greenock
William Fulton / 3 / orphan / Greenock
1861 Greenock Middle, 23 Market St
Household 45
Peter Mechan / 30 / Dock Labourer / Ireland
Catherine Mechan / 30 / Greenock
1861 Greenock Middle, 23 Market St
Household 42
Elizabeth Kelly / 62 / Greenock
William Kelly (previously Fulton?) / 12 / Greenock
1868 Elizabeth Kelly, maiden name Wilkie died at Greenock. The informant was her daughter, Catherine Mechan.
1871 Catherine Meehan, maiden name Kelly, married to Patrick Meehan, died aged 35 at Greenock. Her parents were Archibald Kelly and Elizabeth Kelly, maiden name Wilkie.
1871 Greenock Middle, 19 Market Street
Patrick Mechan / 40 / Labourer / Ireland
Mary Mechan / 60 / sister / Ireland
William Keth (Kelly?) / 23 / visitor / Greenock