All that can presently (December 2022) be gleaned about
Madge O'Brien from sheet music covers and by Internet searching is that she was presumably an American actress/singer who has been featured on 2 works published between 1903 and 1909.
Her portrait on the left is taken from
Monkey Doodle Dandy (1909) music by
Henry Frantzen, words by Jack Drislane and published by
F. B. Haviland Publishing Co. Inc., New York, USA.
Surfers are welcome to contribute any further information about this performer.