So far the controller adapters I have seen for the Atari 5200 and that can provide analog control use a used a digital potentiomenter (and extra capacitance). 

This is certainly a nice solution but there are other alternatives, though:

1) Keep series resistor constant, vary the voltage applied to charge the capactor (just like the trackball do)

That can be done with a PWM providing 0-5V and some resistors in a network to match the desired voltage range. This method is used on the CX-53 trackball. 

2) Detect when capacitors start to charge and hold the line down until the desired count, then push the line to +5V

It is a pity that the architecture of the Pokey Chip, used by the Atarti 5200 to read the potentiometers do not discharge the capacitors at the beginning of the sampling cycle but at the end. The only mark of the beginning of the charge is that the voltage over the capacitor starts to ramp up and that can be done by the analog comparator of a microcontroller set to a voltage that is below the minimum Vih (1.9V). Luckly there is plenty of time to react to that, as the pokey counts in Hsync lines (64us ).