Angel's Prayer

Yui, codename "The Killing Doll" is a matchless assassin, programmed with an emotional override that makes him little more than a puppet. Hired out by a ruthless corporation, Yui loses control of himself whenever there's a job to be done. In the precious few moments he has to himself, he tries to build a life for himself with the guidance of a priest and fellow assassin, Miyagi.

(Source: MangaUpdates)