Irish Americans did indeed face a wave of discrimination during the 1840s and 50s, much of it not unreasonable, since the Irish presented, at the time, social problems very similar to those of the urban underclass today. PC ignoring of such problems and their relationship to ethnicity had yet to develop.
The "No Irish need apply" signs and want ads being widespread is an urban legend. Here is an absolutely fascinating study pretty thoroughly destroying the myth.
http://tigger.uic.edu/~rjensen/no-irish.htm
The Irish, despite genuine prejudice against them and the handicap of their underclass status and habits, worked their way out of this bind by their own efforts. Here is another fascinating article on how they accomplished this, perhaps the classic example of an ethnic group pulling themselves up by their own bootstraps. I found the section about the very real social pathologies of the mid-19th century Irish particularly interesting.
http://www.city-journal.org/html/7_2_a2.html
thanks for those links