Not really possible given the large amount of natives and slaves. But you can certainly play with the demographics to make it whiter.
1) Dramatically screw over the US. Have it be an unstable, decentralized, oligarchal mess that descends into civil war ever 10 years or so like OTL Mexico. That will lessen the amount of immigrants going there.
2) Delay the independence of Latin America (delay or prevent the French Revolution and critically prevent Ferdinand VII from getting the throne), allowing for the stability of the late colonial era to continue. Immigration was already on the upswing, and the economic reforms + stability would gave way to increased urbanization, higher wages, and a small native manufacturing sector.
3) Keep Latin America stable for the next few decades. Combined with its rapidly growing and integrated economy in the wake of the late 1700s situation continuing, and the region will look very appealing to European migrants who want land, prestige and money.
4) Ban slavery. Millions of slaves were still coming in up until the 1860s, legally or not.
This should get millions of more immigrants from Europe and the Middle East in comparison to OTL, altering the demographics. You're still going to get plurality Mestizo areas in many places, but other areas such as Venezuela, the Caribbean, and Mexico will look very different.