Debt
The Chinese only own about 8% of the US Federal Debt. We don't owe them that much and they know as well as anyone that if they start messing with us over that they're going to lose more than they gain.
The question? How do we not burn coal? Simple, we get energy from other sources. I'm not proposing that all coal plants be shut down tomorrow, just that a credible plan be developed to phase them out.