I am unsure if you have looked at the records available in Ireland, so forgive me if I am covering what you have already done.
Irishgenealogy.ie is a free site it covers civil registeration which started in 1864 for Catholics. It would be a good place to start, if the marriage was before that you may find the marriage on Rootsireland.ie, it is a subscription site, but you can sign up for a short time frame, not all the fathers are listed but I hope you are lucky. Take a look at https://www.libertyellisfoundation.org this site has the passenger records and hopefully you will find their journey to America, if you do it often states who they left behind and who they are going to.
If you cannot find details of their marriage, try and widen the family tree to include younger brother and sisters and that way you may find the details of the previous generation. Look for their deaths and see who was present when they died, it also helps you tie up the relationships. Keep an eye out for burial records on sites such as historicgraves.com as volunteers are recording and putting the details up online all the time. On askaboutireland.ie you will find griffiths valuation, this site details the farms that were rented and the valuation was taken between 1847 & 1864, it wont definitely identify your family unless you know their first names, but if you find them it will give you an indication of the size of farm they had if they were farmers.
Use records available on https://genealogy.nationalarchives.ie, look at the wills and the will extracts as I have found deaths that were not registered sometimes included on the will registers.
In America loook at the death certificates some include names of parents, likewise look at naturalization papers.
You can also contact Cavan Genealogy Centre they undertake commissions and may be able to help you further.
1st Floor, Johnston Central Library, Farnham St., Cavan
Tel: +353 (0) 49 4361094
I hope I have give you some direction.
Regards Carmel O'Callaghan