It's great to hear that you are researching your Irish ancestry. With regard to passenger lists, you may find these two websites to be helpful in your search: Immigrant ships
More generally, in 1864 civil registration was introduced in Ireland, which is when we started seeing the formal registration of births, marriages, adoptions, and deaths. These records have been kept at the General Register Office of Ireland (GRO), to this day. Here is a link
with more information.
In addition, we hope that one of our forum experts may be able to steer you in the right direction. Best of luck with your research and please do let me know if I can be of any further assistance.