My father (born 1916) sang it around the house with the notes descending on "cockles" and on "mussels"

In O'Neill's Music of Ireland (c. 1895), the notes ascend.

I find it interesting that Americans sing "She died of a fever, and no one could save her," which doesn't rhyme. However, I believe that not so long ago, "fever" was pronounced "favor."

In a songbook I bought in Ireland recently, the words are "she died of a fever, and none could relieve her." How nice to get rid of that awkward spot after all these years!