Thanks for your help. This is the Cornelius that I am looking for...as well as his wife Bridget Kennelly. http://churchrecords.irishgenealogy.ie/churchrecords/details...
According to 1901 - 1911 census my Cornelius was born around 1836. It would be nice to know if some of the Cunninghams that show up from your link were related but I think unless I can find some more about my Cornelius I might be stuck here. I know that they did move nearby to County Limerick.