Hmmmm. I take a shot at it. First I would disassemble the existing bin. Then rebuild it with a slanted floor.
The slant does not have to be on a 45° degree angle as you can pull the coal to the door with a rake or hoe.
Build the front wall with heavier framing than the side walls, as the slant does load the front wall heavier than the side walls will.
Use these on the corners. To reinforce them. http://www.homedepot.com/p/Simpson-Strong-Tie-14-Gauge-6-in-x-6-in-L-Strap-66L/100374887?N=25ecodZ5yc1vZaqta
Have a door that you can open and shovel the coal out of and into your buckets.
If you can find a couple pallet protector sheets you could attach them to the floor of the bin to get the coal to slide easier.
Or you could build a vacuum loader system and just repair the bin.