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You mean right now? It would probably vary over time depending on whose tracks coal is being mined near. Coal shippers will use whichever railways serves their areas.
More than 40% of U.S. coal production comes from the Powder River Basin of Wyoming, and the majority of that traffic goes over the BNSF, so that would be my first guess. (#2 would likely be the Union Pacific, which serves a smaller part of the Powder River Basin.)
Pennsylvania, West Virginia, and Kentucky account of only about a quarter of U.S. coal production, and the remainder is widely scattered.
Much of the coal from that part of the world is transported by barge along the Ohio River and its tributaries, so that makes rail’s contribution even less.
This doesn’t directly answer the OP’s question, but it may provide an interesting comparision.
In my region is the railway that carries the most coal in Australia: the part of the Main North railway line between Newcastle and Muswellbrook. It carries up to 150 million tons of coal per year, and its contrbution to the transport of coal is described in Hunter Valley Coal Chain. I doubt if there are many two-track railway lines in the world that carry much more coal than that.
The Richards Bay Coal Line in South Africa is the second-largest in the world and did 62 mt in 2010, so yeah, probably not.
In the US, BNSF and CSX.
I recently read an article about coal hauling in the US, and the number of trains running is amazing. Several mile-or-more-long trains a day from even one coal field. That’s a lot of coal!
Yeah, Kansas City Power and Light fires with coal. I once heard that a hundred-car train arrives every hour from Wyoming and Montana. And then they all go back empty. Maybe an exaggeration, but I used to see a moving train every time I drove through North KC.
There is so much rail traffic on the line along the Platte River in central Nebraska, it seems like the trains are longer than the gaps between them. When the crossing gates to up, you have to get through quickly.
When I was working at Great Northern/Burlington Northern, long unit trains (coal only) from Powder River Basin in Wyoming to one customer (Detroit Edison) made up about 20% of the traffic on the whole railroad.
In Q1 of 2015 BNSF transported 604,000 carloads of coal, UP 399k, CSX 289k and NS 277k among the four biggest US railroads. All the other ‘Class 1’s’ including the two big Canadian railroads were much smaller.
http://blogs.oliverwyman.com/rail/wp-content/uploads/sites/4/2015/06/Oliver-Wyman-2015-Q1_-Class-I-Rail-Summary.pdf
You could also measure by ton-mile (one ton transported one mile) but it would probably extend BNSF/UP dominance, because the hauls from the Powder River Basin, where a lot of BNSF and UP coal originates, to destinations or hand off to other railroads tend to be longer than coal hauls by the eastern railroads.
About 70% of the ~1 bil tons per year of coal produced in the US gets transported by train for at least part of its journey to market. Most that doesn’t ever go by train goes by barge, though some coal is burned in power plants adjacent to mines and only ever travels in trucks or on conveyors.
Just for comparison coal production in China was also around 1 bil ton/yr only 15 yrs ago but is now more like 4 bil ton/yr.