Unfortunately there are no civil registrations records in Ireland before 1864 to find the birth records for your ancestors and no surviving census records before 1901.
There are no records in Ireland about who emigrated, where they went, when or what happened to them after emigration.
Church parish records for their religious denomination and birthplace in Ireland, i.e. the town/townland, civil parish and county, that survive are possible sources for baptismal records for them. Irish church parish records aren't computerised or available online.
Here's a map of Ireland showing the 32 counties:http://philnorf.tripod.com/ireland.htm
And there's a list of the names of the 64,000 towns and townlands in Ireland in each of the 32 counties at http://www.seanruad.com
and pick whatever county you're interested in to search.
So you need to research the civil and church records for your Irish born ancestors to identify where they were born in Ireland, i.e. town/townland, civil parish and county, and their religious denomination and their parents names. The records in the US include their civil and church marriage and death records, cemetery records, tombstones, wills and obituaries as well as their US Naturalisation records.
Their children's civil and church birth/baptism, marriage and death records, obituaries may include where their parents were born in Ireland.
All the US census records from 1790 to 1930 are online and fully searchable by surname so you can also search them in the US census records to then locate their civil and church records in the localities where they lived in the US.