There are no records in Ireland about who emigrated, where they went or what happened to them after emigration. Millions of people emigrated from Ireland and went all over the world.
Ships passenger records were handed in at the ports of arrival. If your ancestor was in Massachusettes, you can search the ships passenger records for Boston which are in Boston. Post on the Suffolk County Message Board, the county Boston is located in, about how those records can be accessed.
If you search the US census records for him you will see when he emigrated to the US. The US census records are all online until 1930 fully searchable by surname.
There are no census records surviving in Ireland before 1901. There is no civil registration/vital records before 1864.
Have you searched the US census records for him? His civil and church death records, obituary may include his parents names and where he was born in Ireland. You can search for his US church and civil marriage record to see if that includes his birthplace in Ireland. His children's civil and church birth/baptismal records may include where he was born. His US naturalization records may also include his birthplace in Ireland.
There are 32 counties in Ireland with 64,000 towns and townlands where he may have been born. Because he was born before vital records started in Ireland church parish records for his birthplace in Ireland would be the possible source for a baptismal record for him. Not all church records have survived for all locations for all religious denominations.
There are thousands of parishes in Ireland. Hence you need to find his birth location in Ireland from his US records. to identify what church parish he might have been born in.