I think for the purpose of this discussion fictional stories are fine as well.
They have to have a beginning, middle and end though. So Cats in the Cradle and Ode to Billy Joe certainly qualify. Songs which are descriptive without a time element though are different.
Interesting how far back in time we have to go for these songs, and how many are western themed.
Lastly, I can't think of any solid jazz songs that qualify.