Well the Catherine you have found cannot be the Catherine on the 1840 birth certificate as this Catherine was not born until later....1842.
While Timothy may have been a labourer he had his own house that he rented and did not live in a tenements in the towns as some of his compatriots did. The impact of and faith in religion was very important to these folk and they would be most unlikely to miss baptising a child etc. These would have been recorded by the priests and it is what happened to them since (lost, decayed etc) that makes births hard to find not that they missed a baptism etc.
Anyway back to Cornelius following up on a birth that links to a death in 1885 aged 63 there are quite a few couple on Ancestry!
Cornelius Sweeny
Event Type: Baptism
Baptism Date: 31 Dec 1820
Baptism Place: Mallow, Cork, Ireland
Diocese: Cloyne
Father: Thos Sweeny
Mother: Cath Fogarty
A possible second marriage only put in as the wife has the name Leary and there was a Cornelius Leahy/Leay (with Denis McCarthy) who were witnesses at the marriage in 1865.
Cornelius Sweeny
Gender: Male
Event Type: Marriage
Marriage Date: 17 Feb 1874
Marriage Place: Macroom, Ireland, Ireland
Diocese: Cloyne
Spouse: Johanna Leary
Having a look at the dog licence registrations, also on Ancestry, could be useful as I would have thought a pig buyer would have a dog.