Hi John,
It's great to hear that you are researching your Irish roots. It certainly can be tricky when you back to the first half of the 19th century. This is because before 1864 records were kept in the form of church and parish records; while some of these have regrettably been lost over the years, all the surviving records have been sorted into county-based genealogical centres.
It was only in 1864 that 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.
As your GG grandmother lived in County Mayo, it may be helpful to check out the
genealogy resources available from Mayo County Library. Other members of the Community may also be able to shed some light for you.
Regards,
Eoin