I've tried most of the obvious ones. The girls I know respond well to:
All I Want Is You - try playing it like the Dublin X-mas Lovetown version, with the "sexual healing" bit
In A Little While - especially if you get the guitar lick right instead of strumming.
Swallowed in the Sea - I know it's Coldplay, but girls LOVE it, even if they've never heard it before
One - if you can hit the falsetto at the end without looking or sounding awful this works wonders.
I have blue eyes, and I've dated two girls with brown eyes, so I've played a lot of Sweetest Thing and Brown Eyed Girl. So if the eyes match the song...