hi,
I am afraid offical records for Catholic births in Ireland were not recorded until 1864.
There are older Church records, but you would need to know the name of the parish where Thomas was christened.
There is a record of the baptism of a Thomas MOONEY in Galway in 1832, but I don't know how much information would be on the certificate.
http://ifhf.rootsireland.ie/quis.php?page=1&confirmPageView=Y
There are 6 John MOONEYs recorded in the Tithe Applotment records in the 1830s...
http://titheapplotmentbooks.nationalarchives.ie/search/tab/results.jsp?…
This looks like the family of Thomas and Bridget in 1900, living at
ED 22 Precinct G Cincinnati City Ward 2, Hamilton, Ohio, United States ...
Head Thomas T Mooney M 68 Ireland
Wife Bridget Mooney F 62 Ireland
Son Thomas Mooney M 38 Ohio
Son Martin E Mooney M 35 Ohio
Daughter Mollie Mooney F 34 Ohio
Daughter Katie Mooney F 34 Ohio
Son William Mooney M 29 Ohio
https://familysearch.org/pal:/MM9.1.1/MM8W-FFB
There is a family tree on Ancestry with this family on which is owned by a lady in Kentucky - do you know someone called Medina K ??
Thomas J Mooney
Birth September 1832 in Galway, Ireland
Death 30 Dec 1907 in Cincinnati, Clermont, Ohio, United States
I can send her a message via Ancestry if you would like to contact her.
Thats all I have I am afraid.
Regards,
SEAN