The oldest oral works we have are the Odyssey and the Iliad, and they are about 2,800 years old. Odysseus and Penelope are separated by trials, sea, and time, but they continue to love each other and hope for reunification.

I wonder what a traditional love story is and don't know what is the oldest. But I will put forth the story of David and Bathsheba or Jacob and Rachel as about 2,500 or so years old.