Most of my riding tends to take place round where I live which is on the Mediterranean coast of Turkey as opposed to the Black Sea coast. However, I would recommend reading this post T U R K E Y Our Eastern Blacksea and East Travel 5000 kilometres - ADVrider
There are some good maps and photos later in the report.
I am planning to tour the North East of Turkey and the Black Sea coast this summer.
Regarding tyres in Manavgat, I have no idea but would recommend contacting this chap who is very knowledgable and helpful here in Turkey. https://www.facebook.com/mehmet.avar.12
Please don't apologise for your English. My Russian extends to Natasha and Vladimir, beyond that I am lost