Dear Ann,
I found your query here on Irelandxo. I have searched the Tithe Applotments (dated 1826) for the parish of Fanlobbus, and cannot find any record of Jeremiah O'Leary in the townland of Manch.
I also tried Griffiths Valuations (dated 1852) and found no record of O'Leary or Leary in Manch. The only Jeremiah O'Leary I found was in Knockduff some miles away from Manch. It is only a long shot that they would have been related.
The tithe applotments are a list of land-occupiers only, compiled in the 1820 and may not always include families living in cottages. Griffiths Valuations were compiled in 1852 and are a list of all land-occupiers at that time.
The Catholic Church records can be found online, but they start at 1820. The hand written original records are available in St Patrick's Church, Dunmanway; these date back to April 1803 and are very hard to read as the hand writing is atrocious. I will try to investigate these for you with the hope I can find a birth record for Jeremiah or another of his siblings.
If you ahve any further information on the O'Learys come back to me and I will do my best to help.
Here are some useful links that may be of interest to you.
http://www.corkgen.org/publicgenealogy/cork/titheapplot/
http://www.askaboutireland.ie/griffith-valuation
http://churchrecords.irishgenealogy.ie/churchrecords/search
Yours
Tommy Collins
Dunmanway
Co Cork
Email: tommycollins@eircom.net