Have the countries of Latin America reap the benefits of the postwar economic growth that Western Europe enjoyed. If living standards reach a point where they're even half of the U.S.' few people would want to emigrate.
Perhaps the U.S. pushes for some sort of economic union with the American continent as a bulwark against communism after the war, and establishes a sort of Marshall Plan for the hemisphere. Venezuela, Argentina, Costa Rica and Uruguay already had somewhat high standards of living.
In reality it would just need to encompass the Mexico, the Caribbean and Central America. If we look at the origin of Hispanics in the U.S. two thirds are Mexican in origin, one-fourth are from Central America and Spanish Caribbean, so stabilising this region politically and economically would have helped 90% of the region. This includes 9% of the Hispanics which are Puerto Ricans, but I imagine with a more prosperous Caribbean, Puerto Ricans would have had less of a need to migrate to the mainland.
Also, getting rid of the "war on drugs" would help too, as much of the violence in Mexico, Central America and Colombia has been caused by the drug trade and the smugglers who will do anything to smuggle it to their largest market.