I do not believe what you need is available.

Perhaps your project should be to make your own list from books of the period and with help from your new forum friends.

Here are a few that can get you started:

Crooks, John Joseph, 1842- . History of the Royal Irish Regiment of Artillery. 1914. viii, 367 p., [2] leaves of plates : ill., ports. : Reprint 2006.

G le M. Gretton. The Campaigns and History of the Royal Irish Regiment from 1684 to 1902. 1911. :
file:///G:/E-Books/Regimental%20Histories/British/GRETTON.%20%20CAMPAIGNS%20AN
D%20HISTORY%20OF%20THE%20ROYAL%20IRISH%20REGIMENT.%20%20.pdf

John Jones. An Impartial Narrative of the Most Important Engagements...during the Irish Rebellion, in 1798. 1843. :
http://www.archive.org/stream/impartialnarrati00jone#page/n6/mode/1up

Irish Military History: Free Irish Military History eBooks:
https://irishmilitaryebooks.blogspot.com/

As you find British regiments in Ireland, start looking up their regimental histories - you will find those that were there with in battles, etc. for 1798. Keep adding and then searching the new found ones.

Until 1801 the military units in Ireland were called The Irish Military Establishment.

I will post more materials as I come across them. Other colleagues can do the same or provide regimental names from their own work/research.

Have fun and enjoy your new project.

AvB