I've found several versions of "The Titanic" in Laws' Native American Balladry, but I can't tell if this is one of them or if it's a completely different song floating around... It sounds a lot like D40 I and II.
Here are some of the lyrics:

Oh, the moral of the story, as you can plainly see
Is to wear a life preserver when you sail the ocean sea.
Oh, the great Titanic was, and never more shall be.
It was sad when the great ship went down.
Chorus:
Oh, it was sad__ (oh, it was sad),
Oh, it was sad__ (oh, it was sad),
It was sad when the great ship went down to the bottom of the sea__
(Husbands and wives, little children lost their lives)
It was sad when the great ship went down.