Dublin is quite a big area, but there a few things you can do to get started.
Have you tried checking the Ellis Island records (www.ellisisland.org) or the Castle Garden records (www.castlegarden.org)? Generally, more information was given at the port of arrival rather than the port of departure. If you knew which city they arrived at, this could be a good place to find more information, and perhaps even find out an exact place of origin.
You could also try checking the land records called the Tithe Applotment Books (1823-38) or the later Griffth's Valuation (1848-64). Griffith's is freely available here: www.askaboutireland.com or here: www.failteromhat.com Failte Romhat has lots of other useful links you could try looking at.
Without a more precise location, I cannot check which church records you should check.
Do you know anything else about him, such as an occupation or any other details?
There is a list of Dublin county freeholders and leaseholders dated 1835-37. This is available at the National Library of Ireland, Ms. 9363.
There are Admissions and Discharge registers for Dublin city workhouses (North and South Poor Law Unions). These date from 1840-1938 and can be found at the National Archives of Ireland.
I hope this will help to get you started. Be sure to check any family papers or bibles etc. for any additional information.
Please make sure you link anyone else in your family who is interested in their Irish heritage to our site - and indeed anyone else you know of Irish heritage.
Genealogist (Ireland XO)