I always wondered that myself, as at the hardware store near me I can buy anthracite coal, or Blacksmith Coal, which is a bituminous lump coal.
I was always under the assumption that blacksmiths wanted more of a coke or charcoal though due to the properties in the fuel being imparted to the steel, but I am not a blacksmith and just a machinist/welder.
To that end, I read this in my Great Uncle's Autobiography, written about his life as a boy here in Maine in 1836. It tells how him and his brother made a bartering arrangement for a Base Viol with a blacksmith and what they had to do to make the fuel the blacksmith needed.
Forestalling a little, my chum brother Samuel and I, a few years later, took it into our heads that there should be an accompaniment to that fiddle. Having heard of an ancient cello (“base viol” it was called in those days) that was offered for sale by a blacksmith in Dixmont. We went to see him, got his offer to sell it for 100 bushels of charcoal, if my memory is correct, obtained Father’s consent, closed the bargain with him, and set about its fulfillment, doing the work of burning the charcoal mostly in overtime after doing our regular work. Wood in four-foot lengths was cut by twilight and star light and moonlight, stood up endwise, covered with straw and dirt, set on fire in several places – which were covered after setting, after which came the weary nights of watching for ten or twelve days lest the fire break out, and, getting past control, the kiln is lost. Finally the smoke ceases, a few days smouldering and it is ready for uncovering and raking off. The hay rack is lined with boards, 100 bushels loaded, and the steers haul it to Dixmont, bringing back the cello in its green baize covering, the reward of perseverance.
I am not sure it would be worth it to go through all that today, but I believe charcoal and coke is the preferred fuel for authentic blacksmithing.