Is Mexico city have a stable government?

Relatively so. Mexico City is part of Mexico, a federal presidential representative republic, akin to the United States.

Mexico City itself has a local government, which is elected by the Mexico City voters, but has a great deal of dependence from the federal government. It is stable in the sense that it follows general democratic principles; however, considering Mexico City is a huge megalopolis of 21.2 million inhabitants, it still has weak institutions that can be corrupted or work inefficiently.