Perhaps the Yuan expedition to Java in 1292 succeeds, allowing the Mongols to conquer the eastern half of java and establish some kind of protectorate kingdom there?
You could also have a POD in 1004, with the Khitan defeating the Song army at Chanyuan and succeeding in crossing the yellow river, allowing them to capture Kaifeng and overwhelm large parts of northern China, like Jin did?
Song doesn't have all of the talented generals it did against Jin during this period. No Yue Fei, no Han Shizhong.. I think Liao would have a solid chance at extending it's rule over southern China after it finishes consolidating the north. If that happens, you're likely to have a sort of Kingdom of Tungning situation, with Chinese exiles fleeing to islands like Hainan, Taiwan, and maybe even the Phillippines, so they can regroup and try to reclaim the homeland when an opportunity presents itself. If you'd rather have a more direct connection to China though, you could always have Liao react to such a situation by building a formidable armada to suppress the exile-kingdoms and project power overseas, sort of like how Ming was able to during the treasure voyages.
