WILLIAMSON, W.Va. — If a single moment captured coal country’s despair this year, it was when Bo Copley, a soft-spoken, out-of-work mine maintenance planner, fought tears as he asked Hillary Clinton how, having dismissed coal’s future in language that came back to haunt her, she could “come in here and tell us you’re going to be our friend.”

That was in May. Mr. Copley, 39 and a registered Republican, was “very uncomfortable” with Donald J. Trump then, he said. But over time, in a paradox of the Bible Belt, Mr. Copley, a deeply religious father of three, put his faith in a trash-talking, thrice-married Manhattan real estate mogul as a savior for coal country — and America.

“God has used unjust people to do his will,” Mr. Copley said, explaining his vote.

Now coal country is reckoning with an inconvenient truth: Experts say Mr. Trump’s expansive campaign promise to “put our miners back to work” will be very difficult to keep. Yet as he prepares to move into the Oval Office, Appalachians are eyeing Washington with a feeling they have not had in years: hope.

The American market for coal is shrinking, industry analysts agree. Utility companies have drastically reduced their reliance on coal, in part because of President Obama’s aggressive regulations to cut emissions from power plants, but also because natural gas is cheaper. Nationally, about 300 coal-fired power plants have closed since 2008, according to the National Mining Association, a trade group.