Oni no Hanayome

In Kakuriyo, as the synopsis says, abandoned as a child by her mother, Aoi Tsubaki was raised by her grandfather who shared the same ability, to see ayakashi - spirits from the Hidden Realm, teaching her how to live with the ayakashi in peace. When her grandfather suddenly passes away, Aoi is transported to the Hidden Realm, where the ayakashi reveals himself to be an ogre-god, telling her, that she must pay the price for her grandfather's debt by marrying him. It's a nice, heart warming, slow, romance - slice of life - fantasy adventure anime, reminding me so much of this one as it's the same kawaii love story with a tender ogre husbando. read more 

the art is really so similar. the plot matches as well. one has demons living in japan and other has the zodiac animals and their life with humans. 

In My Happy Marriage, misery seems everlasting in Miyo Saimori's life. Born from an arranged marriage, she was quickly discarded after her mother's tragic death. Her father remarried, and her younger half-sister Kaya received all the affection, while Miyo was degraded to a lowly servant. Lacking the strength to fight against her family's abuse, Miyo loses hope that her luck will ever turn. One day her father summons her to deliver surprising news - she is to marry the head of the distinguished Kudou family. Despite his noble background, Kiyoka is known to be a strict man who has dismissed all of his former fiancées. While arriving at the Kudou household, Miyo expects the same awful treatment as they were treating her at home and to be tossed aside. However, contrary to her assumptions, Kiyoka shows her the kindness and love that she has desperately needed. Although it's not about ogre, the Cinderella drama-love story with a defending husbando who has magic powers, is similar. read more 

Girl is suddenly married off to a seemingly dangerous man, but it ends up being the best thing that ever happened to her. Also, her sister hates her and constantly tries to ruin her life. Both shows also involve supernatural elements.