I have seen quite a few places where a smile plays about one's lips comes up
When Elise saw these things that were so dear to her heart, a smile played about her lips and the blood came back to her cheeks at the thought of being able to save her brothers.
She leaned back, her eyes closed and a light smile played about her lips.
This page has plenty of examples from real-life sources, and so does Google Books.
I can't understand why the preposition "about" appears here, instead of "on." A smile, as far as I understand, should play on one's lip, and play about means to play around. Am I wrong?