Have them take on Guatemala in 1870 when their regime is on the ropes, let there be some sort of (perceived) economic miracle and have the idea of beneficial Mexican rule spread to the rest of Central America. Have Mexico industrialize faster with more international capital, maybe this requires Maximillian to stay in power, but avoiding the civil wars will help. Get Mexico to build the canal with an international company and part-ownership. Leave Panama to Columbia and maybe Costa Rica stays independent. Have the British sell the Mosquito Coast to Mexico and maybe a poorer Jamaica or other series of islands too. An improved merchant marine might also help, though doubtful Hawaii could be come Mexican. If the old Japanese-Mexican ties can be restored maybe they decide to help each other into the 20th century. Have the Mondragon rifle adopted locally and perfected internationally while attracting more talent and international allies. Maybe Mexico develops enough by WWI to work with the UK in exchange for territory or technology, giving the US a headache as they have no desire to fight the UK but also do not want to have a London "Satellite" on their southern border. As a friend of London and Paris they thrive after the war on international trade, promoting education and harvesting local talent. Sonora develops as a major mining center and cross-border traffic is much less than OTL. Mexico dreams of retaking her old provinces to the north but will not do so. By 1950 their standard of living is about better, not that of the US but the gap is half what it is in OTL. Education is mandatory and while the church holds the hearts and minds of the people liberal ideas are discussed and science is explored more in depth. UNAM becomes one of the world's recognized universities and money from petroleum and tourism is put to use for more education and exploration. While Cancun, Acapulco, and Bluefields becomes some of the world's finest destination beaches (especially after the fall of Cuba), the people are not in abject poverty in 2010. Standards of living are akin to some of the Southern US on average and financially they are in debt but not to the same extent as their northern neighbors. Borders run in OTL Mexico, most of Central America, and perhaps Jamaica. Much less likely would be Cuba and Puerto Rico, though they could be satellites if the rebellions against the Spanish saw aid from Mexican gunrunners. Japan would be on very friendly terms and perhaps pre-WWII sees Japanese ships docking at Acapulco or Guyamas, perhaps post-WWII as well.