If you're looking for manga similar to Birthday Presents, you might like these titles. All recommendations are made by Anime-Planet users like you!
Mayuka Fujisawa is lonely. Having lost her parents in a car accident several years ago, she's lived her life alone; she has no friends by her side, and no one she loves. However, one day, Mayuka returns home from school and finds a beautiful man collapsed in her yard - his name is Marshall, and he's a demon who fell from the sky. His red stone pendant is missing along with his wings, and thus he begrudgingly stays with Mayuka for the purpose of home-cooked meals and a place to stay until he can find his stone. Mayuka loves spending time with Marshall and is happy to not be alone again, but she also knows he wants to return to the sky...
Two fantasy one shots telling us two pretty similar stories. Main characters are almost the same - lonely girls, living by themeselves and hoping to find real friends and true love. And those dreams get the chance to come true when young guys appear in the girls' lifes. But something's not okay with the boys.. What? They are just not 100% humans.