Come up with a TL where Islam comes to dominate Mexico and/or South America in with a POD no earlier than 1500.
Or then, it can happen as a cause for the mexican independence war in 1810...the only thing that could be needed is the existence of a muslim revolutionary...
After 1500? Veeeeery hard. Maybe if Morocco somehow decides in 1500 that the only way to defend himself from Spain and Portugal is to modernize and to have an ocean going fleet. He does so, and tries to conquer Canary Islands... And then somehow, after succeding, he sends and expedition to America. There, the Muslims fight the Spaniards with the help of the Amerindians, who rebell, seeing them as their liberators. After winning, the Indians convert to Islam.
if Spain was unified I can't see them very well allowing a Muslim nation / people to colonize so close to their own new world colonies...
It'll be a long process of course. The most possible way to do this is to make Ottoman Empire stronger.And the key factor to realize this is the conquest of Persia by Ottoman Empire. This will prevent the rise of Shiite in Iran to make trouble for OE and also provide resources and population to make OE grow even stronger.