Japanese Ryokan with Private Onsen Search

Find a japenese hotel for a client that meets exact criteria: - Is a Ryokan - Has a private onsen - Has a mountain view or view of trees - Is in between Tokyo and Kyoto geographically - Is available with a private onsen for 2 nights from october 8-10... (Budget: €8 - €30 EUR, Jobs: Google Search, Internet Research, Web Search)