 If you liked
Kami nomi zo Shiru Sekai
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 ...then you might like
Yumekui Merry
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how an other-worldly female creature comes to the human world and a human male helps her hunt down monsters and lets her live with him. in Kami nomi zo shiru sekai Keima is forced to help Elssie hunt down loose souls, but Yumekui Merry Yumeji chooses to help her Merry hunt down dream deamons. and the character Tenri in Kami nomi zo shiru sekai is somewhat similar to the character Kounagi in Yumekui Merry, they both have a mystical female creature in them, Tenri has Dianna and Kounagi has Pati