I sing A Stor Mo Chroi which is a nice song to sing on your own without any backing as the lyrics are quite thoughtful. About someone left in Ireland as their friends and family have left to seek their fortune in far-off lands, and the person is lamenting and singing for them to come back. Roughly translated it means Oh love of my heart. (very roughly)
Or Shule Aroon
Or: Welcoming Paddy Home
Or: Peggy Gordon
or: Sam Hall
Or: The Rare Ould times
and there are loads you could list on and on. It just takes hearing one you like personally to want to sing it. You have to like the song yourself to want to sing it well.
Regards
Ella