Shinigami no Hatsukoi: Botsuraku Kazoku no Reijou wa Ai wo Shiranai Shinigami ni Totsugu

This story is set during the Meiji period in a city were many people are dying. Before their death they all said that they met the God of Death. In order to calm the wrath of the God of Death, Chizuru, the daughter of a fallen family is selected as the sacrificial bride. (Source: natalie.mu, translated)