June:
Records for Ballycallan/Kilmanagh RC parish start mid-1845. (I'm presuming your family was RC).
The 1849 Griffiths Valuation for the family does not show any Hearn entries.
The 1823 Tithe listing for the parish has 174 entries but again no Hearn/Hearne entries. Likely Martin's father was either a labourer or had a very small holding.
Roger McDonnell