The basic idea is to have a main belt with coal and to use pushers to take coal off the belt and feed it to the power plants.
Simple automation will disable the plant's pusher if the plant already has enough coal(I set the limit to 2 to account for inconsistent coal supply but honestly 1 should be fine too).
Keep in mind that due to signal delay and belt travel time you'll get more than one coal per plant when the signal flips to green but it should be around 2-4 coal pieces so still nothing compared to how much coal a plant can stockpile without automation!

Top view should be mostly self explanatory:
I did a curved belt on one side, the alternative would be to offset one side by 1 tile

In side view you can actually see the automation

The inventory reader is hooked up to the coal plant above it and is reading coal count(no surprise there I hope).

The decider is receiving the signal from the inventory reader(the one piece of signal cable seems necessary, I couldn't get the signal to travel otherwise), as mentioned before the condition is arbitrary, <1 should work too. The decider output is linked to the plants assigned pusher, simple as.

Final dimensions are 3x11x5.

This is my first guide and frankly, I didn't put much effort into writing it so please be kind.