This is going to be pretty difficult, but...
I've been wondering if there's any way at all that Native Americans could have managed to resist the Europeans who tried to take over their land. They suffered debilitating disadvantages; their weaponry was inferior, they had no established civilizations, and, of course, they were very susceptible to the diseases that the Europeans introduced. Could they, however, have recognized the threat they faced and banded together, at least in some areas?
Could we, possibly, see confederacies like the Iroquois rising up to meet the white man's threat? Maybe the Seminoles uniting with black slaves and other tribes to beat the Spanish, or the groups of the Great Plains forming a federation to combat the British or the French? While the Native Americans would(and did) face an uphill fight, they were great warriors and would have known their terrain extremely well, and as history shows, they did manage to get their hands on European guns and horses and use them against their enemies.
So with horses, a decent number of European weapons, and good leadership, could the Native Americans have formed alliances and so manage to beat the Europeans off?