Kalliope

Kah-lie-uh-peeh is the pronunciation I hear most when I encounter videos about Greek mythology, and seems to be what Wikipedia gives if I'm reading their IPA key correctly. Kal-ee-yope is one you should watch out for, as that's typically used for the instrument (both are used for the instrument actually, but you'll see that second pronunciation more associated with it). So keep that in mind, unless perhaps you're naming someone real/fictional with the instrument in mind.

English pronunciation - kuh-LIE-uh-pee.

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Edit: why yall down voting my comment? This is, infact, the English pronunciation, and if you need proof, check Calliope 🙄.

This is my name and I've always pronounced it as 'kahl-EYE-oh-pay', but my friends just call me Kalli (ka-LEE). I think it has a very elegant ring to it and I love the meaning of it as well.

I had a Greek friend with this name, it's pronounced "KAL-EE-OH-PAY"

In ancient Greek, probably pronounced kah-lee-oh-peh, with the emphasis on the "oh".

As it is a Hellenic (Greek) name, and also my name, the correct pronunciation of it is: Ka-llyi-oh-pyi. Some other linguists however relate it to beautiful eyes from the present perfect tense of the verb "see" (simple present: orao (type A), oro (type B), opopa (present perfect) and opthalmos which is the eye in Ancient Hellenic) and some others to beautiful face from "opsis".

From my limited knowledge in Greek mythology, I believe it is pronounced something like kall-eye-oh-pee or kahl-eye-oh-pee.