Are you currently in Oaxaca? The local gringo cafes, Cafe Brujula and Cafe Los Cuiles, generally have postings from locals renting out rooms. I would possibly contact
Oaxaca Language Schools - Becari Language School - Oaxaca, Mexico to see if they know of any rooms to rent. I went to that language school and they always had postings.
Do you speak Spanish? You'll get better rates if you do- the English speakers tend to mark up their rates (though still cheaper), not to mention that in my 3 months of living there for study abroad, only a handful of people spoke English. You must know, though, that Oaxaca is anything but quiet so don't expect that. Mexico on the whole has a different level of volume for life that you have to get used to. I lived in a relatively quiet area on the outskirts of town and was woken up every morning at 6AM by the water truck and heard the trash truck and gas truck come by during the day as well. People make their livelihoods by selling things like water and gas off the back of the truck and they yell through the street with their wares- often accompanied by a megaphone and song. You will get very familiar with the "Gas de Oaxaca" song. :P