The last episode of the anime confirms that there are 9, and shows us who they are, including the three we haven't met yet. The two we HAVE met, as flannan said, are Leen, the fairy, and Sue, the duke's daughter. I'm not quite sure on the timeline, but we should be meeting 2 of the other fiancees before the storyline which causes Touya to accept Sue as a fiancee, and Leen doesn't declare herself a fiancee until they discover the Library of Babylon, which might not be until after we meet the 9th girl.
Also, there are only 9 official fiancees, which is why there are also 9 pieces of Babylon and 9 Gynoids. Each Gynoid has inherited one of the traits of their creator Regina Babylon, and Cesca got her perverted sense of humor, so take whatever she says with a grain of salt.