I know my love
I know where I'm going
Siúl a Rún
If I Were a Blackbird
Carrickfergus
The Parting Glass
Will Ye Go, Lassie, Go

Careful of I Dreamt I Dwelt, by the way, it's regarded as an unlucky song, as are Green Grow the Rushes, and especially Cailín Deas Crúite na mBó.