My grandmother was the daughter of German emigrants. When I would stay with my grandparents at the Oregon coast, she would wake me with:
Good morning merry [Mary??] sunshine,
how are you this fine day?

All I can remember, and the second line is noticeably different from all the above. Perhaps she too had modified the song over time from its original lines. I do feel as seems to be discussed elsewhere that it originated with the Germans in some form or another. German author maybe?