If one were to generalize from muzafer sherif's study of conflict resolution between two groups of campers, the best way for the united states and china to improve their relationship would be to

The best way:  Have some superordinate goal (as Sherif termed it) that they needed to pursue together.  A "superordinate" goal is something superior or essential that will cause groups in conflict to come together to pursue that goal.  So, for instance, in US and China relations currently, if climate change were creating a crisis threatening both countries and the world, forcing them to work together on a solution, that would be a superordinate goal.  Or it could be a superordinate goal to achieve something together that they could not achieve on their own.  Let's say conducting a manned space mission to Mars was a goal both countries had but needed each other in order to achieve it.

In the case of the campers' experiment conducted by Sherif, the superordinate goal was restoring drinking water supply to the camp.