Hi,
Key to being able to find the correct records is ganing an understnading of the record keeping background in Ireland. The Irish Genealogy toolkit http://www.irish-genealogy-toolkit.com/index.html will help you understand what records there are and where to find them.
They have excellent articles geared to help those doing genealogy in Ireland and give lots of pointers, explanations and suggestions.
The site Irishtimes http://www.irishtimes.com/ancestor/surname/ can help to identify where the last name was located and uses the Giffths Valuation to identify the name to various counties, parishes, etc... This will also give a lot of variations in the spelling of the name.
You might be able to find a lead for Robert based on when he was in Dublin at the Griffths Valuation itself.http://www.askaboutireland.ie/griffith-valuation/index.xml?action=nameSearch This valuation only runs from 1847-1864, but can be used in reverse sometimes to help identify family members left behind.
A very useful amount of guides are found at http://www.proni.gov.uk/index/research_and_records_held/catalogues_guides_indexes_and_leaflets/online_guides_and_indexes.htm that further give guidance once a general area is found. The "PRONI guide to Church Records, will help you to identify what churches are in what parish" once you pin down the Adams borthers locations.
One other item to look at is google books, modify the search under the search tools to free ebooks and try several combinations of phrases using either of the 2 brothers data that you do know in New York and surrounding states. I''ve been able to find historical bios on family written in the 1800's this way. These can be used as clues, but do need proofing as there are sometimes unintended mistakes.
Good Luck in your search! Jeanette