humm either a female targeted dating offer or a custom LP comes to mind.
ewa would have a whole bunch of dating offers, i'd recommend rotating LPs, seeing what converts, and optimize from there onwards
Being clever... if you have access to the fan page, for example, Facebook Fan-page, you can add some polls, check what their interests are, then divide the database, and on those results you made as many polls as you need in order to understand what do they want.
Content gateway. Depends on your content though whether that would work well for you.
Otherwise there are some FB-specific campaigns floating around, like PageRage.