Hours at most.
The electrical grid is a constant balancing act to match the amount of electricity generated with the amount that's consumed. There's a great deal of automation here, but it still requires human intervention, particularly when dealing with the unexpected.
99.9% of the population dying in a 24-hour period is certainly one of those unexpected situations. There will be an abrupt drop in power consumption, and once the ability of automated systems to compensate is exceeded, the grid voltage will rise. This will trigger various safeguards: sections of the grid will disconnect from each other and power plants will shut down.
Since you specify coal power plants, things will be especially bad. Coal can't adapt to rapid changes in demand the way gas or hydroelectric can. There's almost no hope that isolated pieces will stabilize themselves long enough to run out of coal. Instead, all you'll have left are individual buildings with their own solar or wind systems.