Matthew is right.  A few coal miners can learn to code, but not before going back to school at the graduate or post graduate level.  The large majority of those living in mining country are poor, have a not up-to-date high school education or less, lack the money and accessibility of a good college, and are no longer young.  Furthermore, the field is highly competitive.  Companies hire only the most talented people.  Moreover, there is likely to be a huge cultural barrier.  People age 40 and up, used to living in a small town, very conservative, are not going to fit into the GenX and Millennial culture prevalent in major cities and their outlying suburbs.  Coal miners, unless young, single, and adventurous, tend to be tied to the land and their generations of family before them.  
I'm not saying coal miners are stupid.  They aren't!  They posses a grit, toughness, tenacity, and lots of common sense---the latter absent from the corporate environment.  There are different types of intelligences, not just academic book-learning.
The entire idea is as ludicrous as in 2016 when Hillary brought her campaign entourage to Williamson, West Virginia "the anthracite capital of the U.S.A.," home to the "anthracite mansion!"  (Yes, it's really called Williamson!)  Those who came to her campaign were there to heckle her out of town, something they accomplished very quickly!  
Had Trump lost the election  however, I can guarantee the mountain people wouldn't have tearfully run amok through the streets screaming, "Not my president!" and, "Hey! Hey!  Ho! Ho!  Donald Trump has got to go!"  Instead, they'd be rallying their forces, preparing to fight.  

If you aren't formally educated in programming then you need to be very intelligent or well-suited for it, and you'll still have a much harder time getting interviews. And companies want young programmers, so even if these coal miners all somehow had a knack for programming and had the time and money to learn it, they'd still have an almost impossible time finding a job. It's just not feasible.

Indeed. And I know what I'm talking about. I believe I have a talent for programming, I've been doing it (even for fun) since I was a teenager, plus I've done nothing else professionally since I was an adult. Nevertheless, I found myself unemployed and couldn't find a job for about 6 months when I was in my early 40's, for the reasons you cite. Few interviews, and even fewer job offers.

If they want to hire someone new to the industry, they want a childless twentysomething who can give his heart and soul to the company. Someone who is healthy, young, whose brain still learns new things quickly, with no baggage. Someone who can pull long hours when necessary. Why would they hire someone in their 40's with 2 years of experience (or 2 years RELEVANT experience) when they can hire a 24 year old with the same or even more *relevant* experience?  Especially since the 24 year old will expect less pay -- and can live with less pay.

Software development is *ridiculously* competitive. And there is no other career where your experience loses value so quickly. Stuff you did just 10 years ago might as well be making horseshoes or wooden wheels for wagon carts. All that experience does no good for your career, and actually causes career harm because you got older while you were doing it :)