I had another thought. How about slow waltzes and airs. They seem to be simple to play, and she could play along with a tin whistle player, etc.

Just a few: (this site has simple notation that could be copied easily)

Red is the Rose
http://sniff.numachi.com/~rickheit/dtrad/pages/tiREDROSE2;ttREDROSE.html

Danny Boy (Londonderry Air)
http://sniff.numachi.com/~rickheit/dtrad/pages/ttDANNYBOY.html

Cockles and Mussels (Molly Malone)
http://sniff.numachi.com/~rickheit/dtrad/pages/tiMOLLYMAL;ttMOLLYMAL.html

The Dark Island
http://sniff.numachi.com/~rickheit/dtrad/pages/tiDARKISLE;ttDARKISLE.html

Sally Gardens (Down By the Salley Gardens)
http://sniff.numachi.com/~rickheit/dtrad/pages/tiSALLYGRD;ttSALLYGRD.html

Shule Aroon
http://sniff.numachi.com/~rickheit/dtrad/pages/tiSHULARN1;ttSHULARN1.html

South Wind
http://sniff.numachi.com/~rickheit/dtrad/pages/tiSOUTHWND;ttSOUTHWND.html

Star of the County Down
http://sniff.numachi.com/~rickheit/dtrad/pages/tiSTARDOWN;ttSTARDOWN.html



Are you sure you don't want some Scottish tunes...
Ye Banks and Braes (my favorite)