Dear Ellen
I think you are luckier than most in that you actually do know the area your folk came from.
Have you thought of researching your family back from your grandparents in Scotland. Census or parish records etc to see how far you can go back in Scotland on both sides you can trace them, this might give you some idea of the dates you would be looking at when they arrived from Ireland, and the estimated year they were born. For example, you cannot assume unless you know for sure that your family were born in Ireland because they have Irish names.
I cannot help you with your search in Ireland, but I can tell you that is surprising how earlier in the 17th century some of these hard working people arrived. I just put, for example, John McShane at random on LDS, and I am not saying this is yours as this is a common name, as is O'Neil:
JOHN MCSHANE
Marriages:
Spouse: MARY MULVANY Family
Marriage: 11 OCT 1875 Dundee, Angus, Scotland
You say you are new and I think you have made a good start by having certificates, so one other aid you do is by entering them, and of course you, sequentially with dates, on a spreadsheet or wordprocessing document and see how you go on and where the gaps are. Dates of birth, place of birth, names, where married, to whom, place of marriage etc. That is how I started. and I researched mine to when they were born in Ireland, and then came to a thudding stop!
I do wish you the very best of luck with your family history,
Pat
Poll