If you're looking for anime similar to Requiem From The Darkness, you might like these titles. All recommendations are made by Anime-Planet users like you!
Firstly these are completely different in tone since Requiem From The Darkness is much more serious, full of scary horror, and has a slow but ongoing plot throughout the show. Folktales from Japan is light in tone, does 3 stories per episode, and has more fun stories (even though some are kinda dark). Both series have many stories about strange, supernatural, and bizarre things that happen around the land. So if you want something fun go for Folktales, for a darker approach choose Requiem. Either show is a win!