Dear Ms. Nelson,
Thank you for posting your request on History Hub!
The United States government did not require captains or masters of vessels to present passenger lists upon arrival until January of 1820. So as a general rule NARA doesn’t have passenger lists for vessels arriving during the time period you seek. The state of Pennsylvania, however, tried to monitor the number of immigrants entering the commonwealth during the colonial period as well as during the initial years of statehood. The Pennsylvania State Archives maintains a microfilm collection on ship's passenger lists arriving at the Port of Philadelphia that may be helpful to your research.
We suggest that you review NARA’s Resources for Genealogists, as well as the History Hub Blog titled Suggestions and Advice for Family History Researchers. Also, the FamilySearch Research wiki for Pennsylvania may be useful.
We hope this is helpful. Best of luck with your family research!
There is a book "White Cargo, The Forgotten History of Britain's White Slaves in America by Don Jordan and Michael Walsh. There is information on the Irish and the bibliography may also be helpful.
On Ancestry - Ships from Ireland to Early America, 1623-1850. Vol. II
Link: https://www.ancestry.com/search/collections/49362/ on it ships Names are listed A-Z the information it contains is the name of the ship usually the Captain's name, Port of entry the date and sometimes the number of passengers or just passengers - NO Passenger Lists- many of the ship's in the 1780-1783 time period were captured by the French or American privateers because of the American Revolution The American Revolution was an epic political and military struggle waged between 1765 and 1783 when 13 of Britain's North American colonies rejected its imperial rule. ... With the assistance of France, the American colonies were able to defeat the British, achieve independence and form the United States of America. A few ships arrived toward the end on 1783 and many more arriving in 1784. One of the ships was the -HIBERINA- arriving in Sept. of 1783
Other information the may help are:
UK, Register of Duties Paid for Apprentices' Indentures, 1710-1811
Web: Chester County, Pennsylvania, Slaves and Indentured Servants Index, 1718 - 1839