You should check out 'Hills Like White Elephants' by Ernest Hemingway. It's a very short but powerful story. It focuses on a couple having a conversation at a train station. Their relationship seems to be at a crossroads, and through their dialogue, you can feel the tension and the love that's still there, though perhaps a bit frayed.
One great short love story is 'The Gift of the Magi' by O. Henry. It tells the story of a young couple, Della and Jim. They are very poor but deeply in love. Della sells her long beautiful hair to buy a chain for Jim's precious watch. Meanwhile, Jim sells his watch to buy combs for Della's hair. It shows how selfless and deep their love is for each other.
A really sweet short love story is 'A Rose for Emily' by William Faulkner. It's about a woman named Emily who lives in the South. Her relationship with a man named Homer is complex. It shows how love can be all - consuming and how it can also be a source of great mystery. The story has elements of Southern Gothic, which adds to its charm.