Lani Hermann, who may or may not lurk here, sings a wonderful song about "The Old Grey Duck" or maybe it's "The Old Grey Goose," about a bird with defective offspring:

"And when the young ones they were born
They had no tails nor bills."

I don't know where she got it, but it is a great song.

There's also "I Went to Market," which has duck and goose verses, and "The Christmas Goose," which features at least two kinds of geese(!).