I did want to mention about both the US census and church records. Generally the Irish didn't emigrate by themselves or they were in areas in the US with other Irish from the home area in Ireland. So when you look at the US census records -- which you can access online through a LDS Family History Centre -- also check for others with the same surname in the immediate area where your family was. So you should look at the detail census sheets for that location and not just the information for your specific ancestor at their specific addy. The online US Federal census has an index.
In church records also note who the sponsors were at various religious events, i.e. baptisms, marriages, because they were often relations or neighbours from Ireland and they may provide additional sources to find where your ancestors originated in Ireland. RC churches often required proof of baptism for other events, i.e. marriages. They're known as "bona fides" and if they kept a record of the proof of baptism for the emigrant from the Irish parish church, then you've got the Irish place of birth. But those are often dependent on how good the priest was at record-keeping and whether the parish itself kept the records. It can vary greatly in the 1800s.
There also may be a parish history in the US, a diocesan history or local area history which you also might check. Sometimes they went into detail about emigrants in the area and where they were from in Ireland.
You also want to find the emigrants' parents names. Families in Ireland often used the same given, i.e. baptismal, names and so the emigrants parents names will help sort out who is who.