A good source for researchers of emigrants from Ireland are the
emigration records held in the Public Records Office of Northern
Ireland.
It would seem that most passenger lists were deposited at the port of
arrival rather than departure. It might be because the powers-that-be
were more concerned with those entering a country rather than those
leaving one.
The most substantial part of the emigration records at PRONI, are
letters from emigrants to their relations and friends in Ulster. Some of
these are found in private collections lodged there.
A few passenger lists:
T.3262: Passenger Lists from Belfast, Cork, Limerick, Derry, Newry,
Sligo, Warrenpoint to USA, 1803-06
T.711/1: List of passengers from Warrenpoint and Newry to Philadelphia
and New York, 1791-2
Searchers can find a number of lists of emigrants on the shelves in the
Public Search Room, PRONI.