Dusting off and thumbing through my vast collection of obscura: Try an early English poet named Robert Herrick who wrote a poem in dialogue called A Dialogue Bewtwixt himself and Amarillis. A minor 17th century poet named Andrew Marvell has a Dialogue between Body and Soul,
There is a good deal of Byzantine/Syrian poetry in dialogue form, especialy on religious themes: Joseph and Mary, Cain and Abel, Abraham and Isaac, etc.
I recall a Sylvia Plath poem - very depressing of course - called A Dialogue Between a Ghost and a Priest.
When I was a composer, I once had a series of songs in antiphony: one voice used an original text, the other a translation into another language of the same text. But the music was in very different styles: if the original was e.g. an ancient Greek poem, I used a style evoking that era, but in the translation the music was "modern-sounding."