Hi Tim,
The free parish records on FindmyPast show a Cornelius Lenahan baptised on 3 Feb 1839 Monagea RC parish, County Limerick, the child of John Lenahan and Margaret Hanagan:
(https://www.findmypast.ie/transcript?id=IRE%2FPRS%2FBAP%2F4386602). The birth date is later than you thought but it still could be him as several birth dates given on census/marriage/death records are rough estimates. His godparents's names are difficult to make out but they look like Patrick and Maria Harnett, who were likely some relation.
In the same RC Parish of Monagea, on 16 Jan 1830, a Cornelius Lenihan married Maria Maune. He could have been an uncle of the younger Cornelius.
In the townland of Ballymonagh, Monagea Parish, a James Lenehan married Mary Curtin on 11 Oct 1843 (https://www.findmypast.ie/transcript?id=IRE%2FPRS%2FMAR%2F1358487%2F1). Children were :
Johanna B. 7 Oct 1846 (https://www.findmypast.ie/transcript?id=IRE%2FPRS%2FBAP%2F6130639)
John B. 8 Aug 1853 (https://www.findmypast.ie/transcript?id=IRE%2FPRS%2FBAP%2F6130772)
Patrick B. 1 Aug 1856 (https://www.findmypast.ie/transcript?id=IRE%2FPRS%2FBAP%2F6130772)
James B. 7 Feb 1858 (https://www.findmypast.ie/transcript?id=IRE%2FPRS%2FBAP%2F4386602)
Daniel B. 6 Jan 1861 (https://www.findmypast.ie/transcript?id=IRE%2FPRS%2FBAP%2F6687318)
(Godparents names available on each register)
Hope some of this helps!
Alicia
