An Archdemon's (Friend's) Dilemma: How to Babysit a Crybaby Knight Vol. 1 by Fuminori Teshima

Archdemon Zagan hires his unsavory friend, the sorcerer known as Purgatory Barbatos, to guard Archangel Chastille Lillqvist from the shadows. Barbatos takes to watching over the girl—which really means watching her constantly screw things up, trust people she shouldn’t, and inevitably bawl her eyes out. But something about Chastille and her waterworks may just have a special effect on the sourpuss sorcerer...

The tale of this odd couple begins after the seventh volume of An Archdemon’s Dilemma: How to Love Your Elf Bride!