Aa! Megami-sama! (TV), Happy World! Recommendations
Both are about a boy and a female who is a holy being as they slowly fall in love and the ups and downs they face along the way
Angel or goddess? the important thing is that in both stories they appear to rid the main characters of their unlucky lives, and the innocence of the two cause funny and amusing situations.
Animes where a goddess/angel girl comes from heaven to help a boy and then starts living with him.