Kamisama Mou Sukoshi Dake I've only watched the first episode yet but I think there should be plenty of tearjerk moments.
The Suspicious Housekeeper starts on a pretty tragic premice (the suicide of a homemaker) but ends in a much better place. The youngest kid emoted a degree of despair no kid should even be aware of, she made me cry.
I usually avoid tragic dramas but I have two recommendations for you.
1) Scarlet heart.
2) A werewolf boy, this is one is actually a movie starring song joong ki and park Bo young. It's one of my favouraite korean movie ever. You will both smile and cry like a crazy while watching it