Backing Irish Traditional Music is not as simple as backing some other forms of Western music. Remember to play quietly while you are getting your bearings. There is nothing wrong with droning on the tonic note or laying out altogether on tunes you do not know well. Tunes generally go around a few times (i.e. repeat AABB patterns for example, so listen for a round and then try something quitely on the second go-round.)
|Lawrence Irish Session
Some tunes modulate to different keys so watch out!
Tunes in Major keys e.g. D major, G major : Base backing on normal I, IV, V chords
Tunes in Dorian Mode e.g. E Dorian : Base backing on I, VII, VI. I.e. For E Dorian, E, D, C
Tunes in Mixolydian Mode e.g. G Mixolydian : Base backing on I, VII, V. I.e. For G Mixolydian, G, F, C
If it sounds minor, it is more likely to be Dorian than Aeolian (i.e. normal Minor). Try the major form of the flat seventh note of the major scale for whatever your root/tonic is. I.e. for Dorian tunes with an A tonic, try G Major
If it sounds major but the V chord doesn't work, its probably because the tune is in Mixolydian
Take it easy on the 7th (dominant 7seventh chords like G7, A7 etc.). These are a lot less common in Irish music than they are in other forms of music you may be familiar with in the folk traditions.