Yuri can be used to describe any anime or manga series (or other thing, i.e., fan fiction, film, etc.) that shows intense emotional connection, romantic love or physical desire between women. Yuri is not a genre confined by the gender or age of the audience, but by the
perception of the audience. In short, yuri is any story with women (or girls) in love (or lust) with other women (or girls). (This definition is an edited version of
the one that
Yuricon provides.)
Considering that genies are a "magical spirit believed to take human form and serve the person who calls it", I would say that a title which has a character who fits this description would qualify. Some people have said that Aa! Megami-sama! OVA and Shinpi no Sekai El Hazard are genie titles.
