If you check the Fethiye Times website
www.fethiyetimes.com, select Living information/education there is a list of private schools in Fethiye with email addresses and telephone numbers. Perhaps it would be a good idea to contact them and find out if they have any vacancies? I have never seen an ads for schools other than in the large cities as you said. You could post an ad on Daves esl cafe website
www.eslcafe.com/forums and select Turkey. Some of the forum members may have some information for you. I did my TESOL course and have found private teaching but thats really due to my friend who is an english teacher at a school here in Marmaris. Good luck!