Is there a peaceful way to change Mexico's government?

It usually does, using direct popular vote, as Mexico is a presidential federal representative republic, much like the United States.

If you mean to change issues in the Mexican government such as rampant corruption by state and local officials, or malpractices such as purchase of votes in exchange for food and other items, it will take some time as Mexico is trying to make the change from a third-world country into an industrialized nation. Key Word here is time: removing practices that lasted for decades (and in some instances, for centuries) will take a tremendous effort to do.