Well, the research got interesting on this one. I did find several articles that attempt to quantify the difference in total emissions of a coal recharged electric car, versus a gasoline car of equivalent size.
This one simply estimates the output from coal plants versus output from gasoline engines, and assumes that if one drops by a certain percentage, the other will rise by the same percentage, which is way off base.
LightsOnSolar Not too bad, they do point out the efficiencies of large power plants, but they are pushing their solar agenda, and obscure the question of coal versus gasoline.
Scientific American The lack of detail in this article is very disappointing. Like SFGate, they bypass the obvious co2 per mile traveled metric, and point to dirty coal plants, without quantifying anything.
Quora gets closer than anyone, by comparing the relative efficiencies of large power plants to small gasoline engines. They say that the large power plant is roughly twice as efficient as the individual gasoline engine.
That dovetails with my own experience that the larger a power generating plant is, the more efficiently it converts fuel into electricity.
If we take the Quora assertion of 2x increase in efficiency in conversion of fuel to energy that the large power plant has, that means that half the fuel got burned to produce the same amount of energy, as compared to the individual gasoline automobile.
EIA gives a table on CO2 produced by conversion of fuel to BTU: coal at around 200-210 pounds CO2 per million BTU's versus gasoline at around 150 pounds CO2 per BTU. So, yes, coal produces 25% more CO2 per BTU than gasoline, but if you burned half the fuel to produce the same amount of energy, you're still way ahead of the gasoline engine on CO2 emissions.
However, that's for generation of BTU's, not a CO2 per mile traveled figure. The all electric car, using an electric motor, will convert the resulting electricity to movement far more efficiently with far less waste heat, because it doesn't throw away BTU's the way a small gasoline engine does. The gasoline engine produces far more heat than it can convert into energy, and the excess heat that you burn gasoline to get, gets tossed away via your car's radiator.
One reason large power plants are so much more efficient is - they throw away far less heat than small gasoline engines, once you sum up one plant versus 100,000 small gasoline engines.
Consider also that in the US, only about 1/3 of the current power plants are coal, the other fuel burning plants tend to run natural gas that has a CO2 footprint 30% lower than gasoline.
And... unlike gasoline, some areas will give you a discount on kWh by charging during off peak hours, like late at night, when demand is low. Go buy gas at 1 AM, and it costs the same as it does during rush hour.
On the average, ditching a gasoline car for an electric car of equivalent size and capability will lower your carbon transportation footprint by roughly around 40%, once you consider fuel used versus mile traveled, and the two thirds of US power plants that don't burn coal.
Even the hybrids that use a gasoline engine to charge the battery and propel the car, are about 20% more efficient than a pure gas car, more so in city driving where gasoline engines waste a lot of fuel at idle, while the electric engine just waits and consumes nothing.
So, to answer the original question - can coal fired electric cars be made 'cleaner', the answer is: by using an all electric car instead of a gasoline car, you've already cut your CO2 footprint by around 40% right off the top, more so if you do a lot of urban driving.
If your goal is less CO2, you'd be better off focusing less on 'dirty coal' and more on how to get the cost of an electric car down so that more will be sold and used.