It can indeed be a little tricky searching for ancestors that far back in time!
As you say, without complete details from birth, marriage and death certificates which have dates and locations it is difficult to narrow down some of the potentials.
Before 1864 records were kept in the form of church and parish records, all the surviving records have been sorted into
county-based genealogical centres. So, for Dungarvan, Co Waterford,
RootsIreland.ie would be a good place to take a look at.
Have you had a look at the
maritime passenger records, sometimes they hold information on arrivals to America?
There are some other wonderful places to find information on our article on
Irish Genealogy Resources, please feel free to have a look there too.
I hope this gives you some further ideas and inspiration, and hopefully your fellow members and some industry partners will be able to add to this list!