Ai wa Kane Nari
A runaway demon is taken in by a brothel-owning half-angel with no place in the world. That makes it sound more touching than it is. There's not much in terms of emotional development, which unfortunately left me a bit bored and cold. The cat was super cute though, and so was the demon's guardian.
Yuki to Matsu
A country doctor finds a man with his throat slit, bleeding out in the snow, and takes him home. And then they fall super in love and have a ton of sex! And adopt a kid for a while, meet old friends, make some great food, and grow old. No death, but we see them together many years later. I cried. One character is a former prostitute. He'll use this to his advantage at one point (he sleeps with someone to get something even though he's in a relationship), and we also see flashbacks of him with his former lover. He and his current partner are very happy.
Rumspringa no Joukei