This is a sub-genre of the romantic-comedy genre. To qualify, you have to have a single, dateless, nice guy who suddenly finds himself surrounded by a bunch of hot girls/women who are interested or attracted to him to varying degrees. The male lead may also live with many of these girls.
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.
