I have mixed views on the future ability of Taiwan to defend itself without foreign help, which rather changes the scenario into the Chinese government falls after a war with at least one other major power.
However if we go for a historical situation, perhaps around or just after the Tianamen square protests the government of Taiwan declares independence then. Seeking to divert attention from domestic problems the government of China hastily invades and makes a real hash of it, heavy losses at land and in the sea, massive civilian casualties in Taiwan and global revulsion are the result. This is probably the sort of situation in which the Chinese government is most vulnerable, but even then it relies on the invasion being the final straw and not underlying cause.
However if we go for a historical situation, perhaps around or just after the Tianamen square protests the government of Taiwan declares independence then. Seeking to divert attention from domestic problems the government of China hastily invades and makes a real hash of it, heavy losses at land and in the sea, massive civilian casualties in Taiwan and global revulsion are the result. This is probably the sort of situation in which the Chinese government is most vulnerable, but even then it relies on the invasion being the final straw and not underlying cause.