I was thinking that one of the following could work:
A) China or Japan decide to join Europe in the colonization of the New World and colonize much of the west coast, while at the same time introducing various religions from East Asia, such as Buddhism, Confucianism, and Shinto.
B) During the Latin American Wars for Independence, a Quechua man gains support and crowns himself Sapa Inka, forming a new Inca Empire, with a neo-Intiist faith being the main religion of the Second Empire.
C) During the American Revolution, a religion similar to the Cult of Reason during the French Revolution becomes very popular, and replaces most Christianity.
D) A Jewish state is formed in the Americas instead of Israel.