A poem with two voices is a piece with two personae, one of whom may be the poet, speaking. Writing an original poem for two voices -- that is, two characters speaking in one poem -- has many approaches, but the easiest method is to use more than one author's voice in a single piece.
Classic Duo-Voice Examples
The two-voice poem reveals the limited viewpoint of one speaker's character through the voice of another. The best examples are early ballads like "The Unquiet Grave" and Keats' remarkable "La Belle Dame Sans Merci." The first is a conversation between a lamenting man and his dead lover's ghost; the second is an interview between a love-sick knight and an unconcerned observer. In both poems, the grief-stricken men are obsessed with their lost women. The other voices remind them that mortal love does not last.
Begin Writing by Improvising
Writers Leigh and Cramer give excellent examples of some side-by-side methods of writing two-voiced poetry. However, the easiest way is for you to create an argument as a dialogue. You can write it as a narrative or dramatic scene. For inspiration, you can get a group of friends to improvise and record several confrontations. The dialogues can be heated arguments, but the ideal mix is to have one passionate speaker and one dispassionate one to show the tonal differences in their opposing points of view.
Improvisation becomes Verse
Once you have cut a dialogue to a usable length, try writing it divided into stanzas, with one speaker per stanza, alternating speakers throughout. Read the poem aloud many times to discover the best diction and cadence for each line. Dialogue is conversation, but poetry is music, so do not be afraid to let the words "sing." They need not rhyme, but if you are particularly adept at that skill, it does add to the music.
Verse Becomes Poetry and Debate
A variation on this method is to write the entire argument of one speaker in the poem's first half, and the second speaker's in the second half, as Keats does. No matter how you do it, remember that you are doing multiple duties as a writer: in addition to creating poetry, you are writing to persuade readers to a viewpoint. This is the fun of the two voice-poem, a work that is at once a dialogue, a poem and a debate.