According to Allmusic.com, Phil Rosenthal sings A DUCK NAMED EARL on the various-artists album "Grandma's Patchwork Quilt: A Children's Sampler." (It was published as a CD in 2003 but I think the original recording was much older. I believe I had that album as a cassette in the early 90s when my son was little.) It's attributed to "Beth Sommers/Traditional." (I assume that means, "words by Beth Sommers, music traditional.")

I transcribed these lyrics from a sound sample:

Earl and Lady Luck had a family.
I decided not to name them very hastily.
Four of them together swam away,
But they still came back to visit with me ev'ry day.

I built my duck a shelter from the cold and the rain.
She swam in the sunshine and ate up all my grain.
You may say that ducks are silly and they have no sense at all,
But Earl would always come to me whenever I would call.

Repertoire.BMI.com says DUCK NAMED EARL was written by Elizabeth Sommers Rosenthal, and published by Sourwood Music.