The original zombie romance?
There’s almost always a part in zombie stories where someone is bit or infected and one of their loved ones has to face a choice: to watch them turn and become dangerous to the rest of the survivors, or shoot them while still human. This is never an easy task. Maybe this happened off screen, and you see the survivor shaken and not quite sane, shocked by what this war with the undead has made them do, and they question themselves and if live is worth living after what they have done.
There are some short stories I’ve read lately which deal with the bond of lovers or family after death. You might question if they are zombies because they might not be precisely called zombies; maybe just undead, reanimated corpses. This is not romance WITH zombies but love for the human-that-is-now-zombie (although one story by Williamson isn’t on this specific theme of love in the time it’s set).
I do think that we can’t be so direct about what a zombie is or isn’t, because authors are bloody inventive creatures and they will force these creatures we once knew to evolve. There’s been quite a few changes in the short 100ish years of the Americanised fictional zombie, and that’s a damned quick evolution from zombiing individuals to mobs (Vampires used to be hidden singular vamps or in small groups, and now are a whole known race in literature with great numbers).
Anywhoos, here’s the stories (I haven’t finished the whole compendium yet, so might add more later):
Was it a dream? by Guy de Maupassant (1910)
The Cairnwell Horror by Chet Williamson (1990)
Later by Michael Marshall Smith (1993)