Thomas:
Welcome to Ireland Reaching Out!
The subscription site Roots Ireland had the 1863 church marriage record for Honora and Jeremiah in Shandrum.See below. Civil registration of RC marriages started in 1864 which is unfortunate in your case because civil marriages list the names of the fathers of the bride and groom. There are six baptismal records for children of Jeremiah and Honora: Charles 1863 Catherine 1865 Callaghan 1867 Honora 1868 Jeremiah 1869 Patrick 1871
I located the 1867 civil birth record for Callaghan McCarthy (eighth record) https://civilrecords.irishgenealogy.ie/churchrecords/images/birth_returns/births_1867/03479/2278615.pdf The family lived in Killabraher townland. There is a Killabraher North and South.
I also located the 1838 baptismal record for Jeremiah McCarthy. See transcription below.
There are three possible baptismal records for Honora in Shandrum: 1837 1840 1842 Not sure which is your ancestor.
Roger McDonnell
Date of Marriage:08-Feb-1863
Parish / District:SHANDRUM
County:Co. Cork
Husband JeremiahMccarthy
Wife HonoraO Connell
Name:Jeremiah MccarthyDate of Birth:
Date of Baptism:13-Mar-1838Address:K BraherParish/District:SHANDRUMGender:MaleCountyCo. Cork
Denomination:Roman Catholic
Father:Charles MccarthyMother:Catherine ConnorsOccupation:
Sponsor 1 /
Informant 1:James LawleeSponsor 2 /
Informant 2:Judith Donohughe