Hello,
Ballard is in Lynally Civil Parish, Kings County.
There is a description
here of the parish in 1837 (a bit early for you but probably not changed too much).
In 1850s - Griffiths Valuation shows the householders of Ballard
here. There is a bit more detail as shown.
Perhaps you will find your family name?
1901 census shows that there were 82 people living in Ballard.
best wishes
heywood