1860 would be a parish record, civil registration started after 1864. Found lots of Jeremiah Gleeson's on the websitewww.familysearch.org
Needs lots more researchwww.askaboutireland.ie
In 1852 in Cork the Griffith Valuation took place. There were 58 Gleesons. None lived in the Parish of Rathgoggan or the Town of Charleville or Part of Charleville, Union of Killmmallock. A poor law union would contain, towns, parishs, townlands within a 12 mi. distance.
So if your information about Charleville came from a marriage certificate it is likely the bride's parish.
I looked in the directories from 1870, 1881 & 1894 no Jeremiah Gleeson
Parish records are available on line with:www.irishgenealogy.ie
(but only North East with roots)
Did they have any son's. As usually first boy named after father.
The only Jeremiah Gleeson of the right age in the 1901 and 1911 Census was never married and a farmerwww.census.nationalarchives.ie
Mary ODonnell age 29 visitor @13 Rathgoggan Middle, Charleville Cork, not married
Thomas ODonnell, 19- Chapel St. Clarleville Cork
Mary ODonnell Mother born Waterford, children born Limerick
19 Commissioners Building (Middleton Urban, Cork)
Hannah Gleeson age 65, widow, born Waterford
Mary 25 Cook domestic
Richard 24 shop porter
John J. 21 shop porter
William 16 shop porter
There are Gleeson's in the current on line telephone book for Cork, 46 and there are 80 Donnell's a address they share is Middleton, Cork.
There wouldn't be many, so I would try that as a start sending a few letters.