There's a guy who does this in Kyoto, but his name escapes me. He is an MK Taxi driver who speaks good English, and while I didn't use him personally, I was always impressed by the customer service of the MK Taxis I did take in Kyoto (drivers leaping across the center console to simply open the door for me in the rain..)

I didn't find him in 5 minutes of Googling, but I did find this other guy who seems to fit your bill. No endorsement from me, but I figured it was a waste to close this tab without sharing with you: http://www.kyoto-doitaxi.com/