Pronunciation of [ə] is notoriously difficult for Japanese speakers, and while trying to communicate its importance in languages such as English and French, I started to wonder: do any dialects of Japanese employ the schwa, or some approximation of it?
There is a dialect of Ryūkyūan employing [ə]:
“The Yaeyama Taketomi-jima dialect has a six-vowel system: a, ə, i, u, o, e. <…> _ə_ is a vowel found only in the Taketom-jima dialect…”
(Handbook of the Ryukyuan Languages)
This implies also the fact that [ə] is notoriously rare even for Ryūkyūan.