Ane no Kawari ni, Yomei Ichinen to Iwareru Koushaku Shisoku-sama to Kon'yaku Suru Koto ni Narimashita

義姉の代わりに、余命一年と言われる侯爵子息様と婚約することになりました

Adaptation

In Sickness and in Health: How I Got Engaged to the Son of a Marquis with One Year Left to Live
Ane no Kawari ni, Yomei Ichinen to Iwareru Koushaku Shisoku-sama to Kon'yaku Suru koto ni narimashita· 義姉の代わりに、余命一年と言われる侯爵子息様と婚約することになりました
manga

Edith is an orphaned girl who is treated coldly by her stepparents and stepsister. One day, her stepsister receives a marriage proposal from Lionel, the eldest son of the highly prestigious Count of Granvelle. However, there is actually a hidden story behind this proposal... and Edith is suddenly engaged in place of her stepsister. "I'm sorry, you can't be engaged to someone like me. Can you just bear with me for a year?" Her fiancé only has a year left to live, and this is a happy love story in which pure love creates a miracle! (Source: Kodansha, translated)