Despite being older than the Catholic Church and having been endorsed by eastern empires, I hadn't seen any Orthodox knightly orders. I know that this may be due to the fact that the Catholic Church was more centralised than it's eastern counterpart, and that in the East most religious matters that required military intervention were handled by the state. Even so, there have been catholic orders that operated in this area, with the support of the locals, so it would be hard to say that the climate wasn't the right one for them, especially with the proximity. Even the Order of the Holy Sepulchre was catholic, despite operating on the lands of the former Eastern Roman Empire.