RH-
"MY GOOD OLD MAN" has been widely recorded. Burl Ives, Richard Dyer-Bennett, Joan Baez (among others). Sharp collected it in 1918, considering it an "English Folk Song from the Southern Appalachians".

Another common American one dealing with a young woman and an old man(which I always thought had English antecedents, is "Old Shoes On and his Leggins"