I searched the Irish Family History Foundation's database. It contains 12,000,000 surviving rcds for abt 65% of Irish counties. Rcds are increasingly sparse B4 1840. Rare B4 1800.
There are many variants of the Hefferin surname. These variants are included in the following searches. There are 6,097 B rcds for this surname, 3,362 in the counties of Kildare, Kilkenny, Cork, and Limerick.
For Edward Hefferin B 1858 in all Ireland, I found 4 B rcds: 1856 Limerick, 1858 Kilkenny, 1861 Meath, and 1862 Galway. None of these recorded a father's name of Edward.
For Charles Hefferin B 1859 dtto, I found 0 B rcds. This is unusual since you state you have his baptismal rcd.
For Edward Hefferin M 1853 +/- 4 yrs ditto, I found 3 M rcds: 1849 Tipperary, 1855 Tipperary, and 1857 Limerick. A view of the detailed M rcds SHOULD show the bride's name and MAY show their parents' names.
For Edward Hefferin B 1833 ditto, I found 4 B rcds: 1830 Kildare, 1831 Cork, 1832 Tipperary, and 1836 Kildare.
Google the Foundation's name to lead you to this database. Pls post your search results to this genforum msg.