While they are not recent compositions, here are four more examples of songs I have heard described as traditional. The last two date back to the 19th century, so maybe they are old enough to have "gone into the tradition." Nevertheless, in all cases the published sheet music exists and the composers are known.

I'll Fly Away, written by Albert E. Brumley.

The Mingulay Boat Song, written Sir Hugh S. Roberton. He adapted the melody from a traditional air.

Oh, Dem [sic] Golden Slippers, written by James Bland.

Drill, Ye Tarriers, Drill, written by Thomas Casey and Charles Connolly.

--- Steve