British Military Units found on the following pages of vol. 2 , Memoirs of the different Rebellions in Ireland from the Arrival of the English, with a Particular Detail of that which broke out the 23rd of May, 1798. : https://archive.org/details/memoirsdifferen02musggoog
I will continue this pursuit as time allows:

p, 92: Monagham militia [col. Durham]; light batallion [col. Clavering];

p. 94: the 64th regiment, and the light batallion consisting the light companies of the Kerry, Dublin, Tipperary, Armagh and Monagham militia, and 150 of the 22nd light dragoons. with two curricle 6-pdrs and two 5 1/2 howitzers;
250 of the Monagham militia, a troop of the 22nd light dragoons, and the Belfast cavalry; and the light battalion from Blaris [col. Clavering], and the dragoons by the honourable col. Lumley;

p. 95: Dunscoverick cavalry,

p. 96: 2nd battalion; 22nd light dragoons;

p. 99: Atrim yeomanry;

p. 100: Royal Irish Artillery; light companies of the Armagh and Monagham militia;

p. 101: Toome yeomanry;

p. 102: Tay fencibles;

p. 103: York fencibles

p. 105 : 22nd dragoons

p. 106: Monagham militia; Argyleshire fencibles, 22nd dragoons

p. 109: [Coleraine] yeomanry; Londondary and Bevagh corps of cavalry;

p. 110: Hertford and Bermingham militias, Cambridge regiment [militia?]

P. 123: a yeomanry corps, commanded by captain Jones, of Ballina;

p. 127: Prince of Wales fencibles
p. 128: Prince of Wales fencibles;

p. 149: Kerry militia; Fraser fencibles; Kilkenny militia;

p. 150: Longford militia; Lord Roden's fencible dragoons, 4 6-pdrs. and a howitzer from Athenry; 100 men from the 6th regiment.; city of limerick regt. of militia; 100th regt.; 1st and 2nd bats.light inft., flank comps. Bucks and Warwick militia;