Hi,
Thank you for your message.
One of the main pieces of information that you need when researching your family history in Ireland is a location. Most Irish record sources- parish records, land records, census records- are based on specific locations. Do you have any documentation belonging to Joseph that mentions a specific place in Dublin where he was born? Until you can find a specific place it may be difficult to determine what records you should be looking at.
Have you looked into Joseph's millitary career? Any military records kept of him may provide you with more information and perhaps even an exact place of origin. To see what UK millitary records are available check the UK National Archives here:
http://www.nationalarchives.gov.uk/records/looking-for-person/
The fact that you know he may have been Roman Catholic is helpful, however as there are a great number of Roman Catholic parishes in Dublin city and county without knowing what parish he belonged to it will be impossible to know where you should be searching.
Do you know Joseph's parent's names? If you do, perhaps you could search for them in Griffith's Valuation. This was a land survery carried out between 1848 and 1864. If the results returned are limited it may help you narrow down the parish that the family may have come from. You can search this here:
http://www.askaboutireland.ie/griffith-valuation/
Some other websites which may help you are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
Genealogy Links: http://www.genealogylinks.net/uk/ireland/dublin/index.html
Family Search: https://familysearch.org/
I hope that this helps. Remember to post any new information that you find. The more information you post, the more likely it is that one of our volunteers will be able to advise or assist you. Also include information concerning which sources you may have already used so others may further your search.
Kind regards,
Genealogy Support