My faculty assistant, a Briercrest College grad and future biblical scholar, Luke Johnson, was kind enough to compose and teach my students a catchy Greek alphabet song using the reconstructed Koine pronunciation. They loved it!
With Luke's permission, I have uploaded his recording here. Luke also sent me a pdf with the chords for anyone with the requisite guitar skills. (The recording may seem a bit fast, but the song can be played slower, and is suited to a call-and-response format.)