The Lynch's of Dublin/Meath (mid 1700s)

I have hit a brick wall, but I appreicate how fortunate I have been to get back so far. 

The earliest ancestor I have found is a man named Alexander Lynch and his wife Ann. They had six children, all baptised Catholic at St. Catherine's on Meath Street, Dublin. 

1. Mary, b. 1748
2. Anastasia, b. 1750
3. James, b 1752
4. Alexander, b 1754
5. Oliver, b 1756
6. Marian, b. 1757

Unfortunately, there is no other information regarding Alexander, his wife, and most of his children. I am directly related to his son Oliver (and was confused by his naming due to Oliver Cromwell's relationship with Ireland). 

Do you guys have any advice on researching the above ancestors - I would really appreicate it.