I would have said (cal-ee-ope) was the correct pronunciation in English. The Greek goddess would be (call-I-oh-pee) but the pronunciation of the original root isn't a good guide to how to pronounce it in English.
According to Steam Boats, this rhyme is supposed to help, but I don't see how - since you can rhyme it with either me or hope!
Proud folk stare after me,
Call me Calliope;
Tooting joy, tooting hope,
I am the calliope.
