Pugwash
The Divine Comedy
The Duckworth Lewis Method

I first note that the general AM site provides the following list of Irish artists:

1 U2
2 My Bloody Valentine
3 Sinéad O'Connor
4 Thin Lizzy
5 Damien Rice
6 Therapy?
7 Planxty
8 Rory Gallagher
9 Virgin Prunes
10 Kate Nash
11 Enya
12 The Cranberries
13 Chauncy Olcott
14 Gilbert O'Sullivan
15 The Chieftains
16 Richard Harris
17 The Boomtown Rats
18 The Thrills
19 Andy Irvine & Paul Brady



Artists bubbling under:
Altan
Christy Moore
Hothouse Flowers
Mellow Candle
Patrick Wolf
Roisin Murphy
The Bothy Band
Whipping Boy

Now, my favorites:

1 U2
2 Sinéad O'Connor
3 The Cranberries
4 Thin Lizzy
5 Gilbert O'Sullivan

"The Men They Couldn't Hang" have some Irish/Scottish stuff (sorry if putting those two together shows me up as a musical ignoramus) going on in their music. I liked them very much when they were around.