I was wondering this after spending some time reading a timeline of a better Mexican Revolution. The thought came to me...was there any possibility that a member of the Spanish Monarchy could have possibly up and pulled a Pedro I, form a new independent nation from the territory consisting of New Spain?
Conservative Mexicans wanted a Spanish prince to be their ruler during the independence (see the Plan of Iguala). Iturbide became the emperor Agustín I when the Bourbons declined the offer because they thought they could still keep Mexico as a Spanish colony at the time. If they sail Mexico instead of remaining in Spain during the Napoleonic wars however, I think you may have a timeline.
EDIT: *Checks Penguin History of Latin America by Edwin Williamson*
For this prospective timeline, you'll have to watch out for Santa Anna. He was the one who pushed for a republic, forcing Emperor Agustín to abdicate (page 226).
Even the liberals within Spain rejected Iguala. Still, the Iguala debacle is well after your proposed point of divergence, so I think your idea has a chance.
Iguala gave many privileges to the Catholic Church, letting it keep its Mexican holdings. Equality between Indians, mestizos and ethnic Spaniards was a part of that plan too, but I am uncertain on the Spanish monarchy's position on race at the time (page 225). Remember that Ferdinand VII is considered one of Spain's worst kings due to his hardheaded nature regarding liberals and the colonies, so your timeline could result in a different kind of chaos for Mexico. . .