You really don't have much to go on.
The only thing I could suggest is to maybe check out
www.brsgenealogy.com It is a good site for old records and has some for John Sliney Cork Births 2 for 1816 , 1 for 1813, 2 for 1812, and 1 for 1810
It is not a free site. You buy credits and pay €5 if you want to see a detailed record for just one entry. Sometimes you might think you have the right one and end up going through two or three before getting the correct one. In your case you actually won't know if you have the right John Sliney or not.
It's a pity you don't have any idea of the parish.
Anyway have a look and see.
Good luck
Mary