Yokai Doctor(2006)

Youkai no Oisha-san

Kotoko is descended from a family of professional exorcists, and she sees her special relationship with yokai - supernatural spirits from Japanese folklore - as a great way to be more popular at school. But then she meets Kuro, a shy loner who happens to have the same talent... and a little something extra: He's a "yokai doctor," and has the ability to not only communicate with the yokai, but also to cure their strange illnesses!

(Source: Del Rey)

Included one-shot:
Volume 12: Kiraboshi Tentou (キラボシ・テントウ)