Laurence Harmon (Harman) (1808-1861) & Bridget Hayes (1813-1866) Family

I have IFHF baptism records for Laurence & Bridget's children: (1) David Harmon 30/01/1831 (addr: Coolnahaha), sponsors: Richard Corcoran and Mary Cashin.  (2) Henry Harmon 14/01/1835 (addr: Smithstown), sponsors: Luke Roach and Anastatia Grant. (3) James Harmon 25/07/1837 (addr: Ballymartin), sponsors Stephen Bergin & Bridget Hayes* - believe this is a typo with Mother/Sponsor transposed: Mother is listed as Anastatia Harmon.  (4) John Harmon 14/03/1840 (addr: Smythstown), sponsors: John Aylward and Ellen Shea.  (5) Laurence Harmon 14/05/1842 (addr: Smithstown), sponsors: Laurence Malone and Bridget Long.  (6) Elizabeth Harmon 10/12/1844 (addr: Ballymartin), sponsors James Laresy and Mary Malone.  (7) David Harmon 6/11/1846 (addr: Ballymartin), sponsors: Thomas Smith and Margaret Holden.

I have been unable to find a birth/baptism record for Thomas Harmon, my gg-grandfather, b. 1834.  He shows up in Ohio in the 1860 census, in Missouri in the 1870 census, and back in Ohio in the 1880 census.  His grave, and those of Laurence and Bridget are all in the Calvary Cemetery, Middletown OH.  (Also a matching headstone for David Harmon, who died in 1871 at 24 years of age.)  I have no proof that Thomas actually was the son of Laurence and Bridget.  Laurence's headstone says he was born in Kilkenny IRL.  In the 1870 census, Thomas and his family also had a David Harmon living with them, listed as a farmhand.  So I wonder if David died in a farm accident within a year, and the family decided to move back to Ohio and bury him with Laurence and Bridget.  Could Thomas have other parents in Kilkenny that someone could suggest?