He was baptized Daniel on August 30, 1848, the youngest child of the family of John O'Neill and Catherine Mahony, who married in Caheragh on April 6, 1834. The Mahonys resided in Kealanine, near Castledonovan.
Catherine's father was known as Daniel O'Mahony Ciánagh Mór. The family were known for their love of music. (I think this is all documented in Captain Francis O'Neill's book on Irish Folk Music. Check the web and Google book archives.)
Catherine's mother was known only as Mary Mahony. I cannot tell if that was also her maiden name. Daniel and Mary both died about 1857. They were eventually interred in Enniskeane. I do not know if that is where these Mahonys were originally from.
The marriage record for Daniel and Mary as well as the baptism records of their children probably have not survived. I did a search for Mahonys as witnesses in the records of the Trawlebane O'Neill family, as well as other Mahonys out of Kealanine, wondering if perhaps they could have been relatives of Catherine.
A Daniel Mahony and a Mary Mahony witnessed the 1834 marriage of John O'Neill and Catherine Mahony.
John Mahony was godfather to Philip O'Neill on January 27, 1835.
Mary Mahony was godmother to Mary O'Neill on July 6, 1836.
Daniel Mahony was godfather to Michael O'Neill on January 15, 1841.
Ellen Mahony was godmother to Catherine O'Neill on September 19, 1843.
A John Mahony married Margaret Hourihane in Drimoleague & Drinagh on March 3, 1840, before witnesses Daniel Mahony and Pat Hourihane. They lived in Kealanine.
The children I could find are Daniel, January 19, 1841 with godparents Daniel Mahony and Mary Mahony; Mary, February 10, 1842, with godparents Daniel Mahony and Ellen Mahony; and Margaret, August 30, 1846, with godparents James McCarthy and Bess Hourihane.
A Norry Mahony from Kealanine married Tim Canty February 22, 1838, with witnesses Daniel Mahony and Tim Canty.
Tim Canty the bridegroom may have also gone by John. **If that is correct**, records show them in Dromasta and Kealanine, and the known children include Margaret Canty, October 28, 1843, godparents Jeremiah Canty and Mary Sweeney; Curly (Cornelius?) Canty, November 13, 1845, godparents Paddy Canty and Mary McCarthy; Ellen Canty, May 21, 1848, godparents Andrew McCarthy and Johanna Mahony; and John Canty, April 25, 1852, godparents Daniel Mahony and Honora Mahony.
A Johanna Mahony married Andrew McCarthy (Sowney) on February 12, 1839, witnesses Daniel Mahony and Mary McCarthy. (I might have Johanna's death record as February 7, 1907, putting her birth year about or before 1821.) Ellen Mahony was godmother to Charles McCarthy baptized September 11, 1840; Dan Mahony was godfather to Johanna McCarthy baptized February 3, 1850.
I have not yet found obvious marriage data for Mary (O'Neill godmother, 1836) or Ellen (O'Neill godmother, 1843).
The O'Mahonys in the ancestry of Captain Francis O'Neill have NOT been conclusively identified in this research expedition. But the data could be circumstantial evidence of a sibling relationship between Catherine Mahony O'Neill, John Mahony, Norry Mahony Canty, and Johanna Mahony McCarthy. There is also some encouraging genetic data from known descendants of Johanna Mahony McCarthy and Catherine Mahony O'Neill showing an excellent match (centiMorgans in the low triple digits). However, rural Ireland being what it is, these two DNA test takers appear to be related in multiple ways. Genetically isolating the Mahony relationship - if there is one - is just not possible with the data currently available.
There are other Mahonys who resided in Kealanine, but their records don't exhibit obvious familial ties to the aforementioned Mahonys. Much more evidence is needed to make a case for the family of Catherine Mahony O'Neill, but at least this is a start.