A friend taught us a clapping gerba (I hope I've spelled that right) from India, about celebrating holi. I thought it was a lot of fun. The kids would enjoy clapping along.
Now, as a true and proud daughter of Pittsburgh Pennsylvania, I would reccomend one of Stephen Foster's songs as true American music. They are not true folk songs. But they were composed in the folk style, and sung by miners, soldiers, farmers, and assorted other ordinary folk. Maybe "Some Folks Do", or "Glendy Burke".