[_hao]

Cyril and Methodius didn't create Cyrillic. That's a very common misconception. They created the Glagolitic[1] alphabet which was a precursor script. Cyrillic was developed later by their students and other scholars in the Preslav Literary School[2]. They named it Cyrillic to honour the brothers, but the brothers themselves didn't create Cyrillic.

[1]: https://en.wikipedia.org/wiki/Glagolitic_script

[2]: https://en.wikipedia.org/wiki/Preslav_Literary_School

EDIT: Sorry, I misread what you wrote. It's late and it's been a long day. You weren't saying the brothers created Cyrillic. As for whether they were Greek/Bulgarian I cannot say. I've read different opinions on that throughout the years. Definitely Byzantine, but anything else I cannot say.