The C-64 uses the SID chip (datasheet) to read the paddles, it has two A/D converters.
The paddles use the wiper and one end of the pot as a simple variable resistance, there are 2200pF capacitors from the A/D inputs to ground.
From the datasheet:
POTX-, POTY (Pins 24,23) — These pins are inputs to
the A/D converters used to digitize the position of
potentiometers. The conversion process is based on the
time constant of a capacitor tied from the POT pin to
ground, charged by a potentiometer tied from the POT
pin to +5 volts. The component values are determined
by:
RC = 4.7 E-4
Where R is the maximum resistance of the pot and C is
the capacitor.
The larger the capacitor, the smaller the POT value jitter.
The recommended values for R and C are 470 KOhms
and 1000 pF.
Note that a separate pot and cap are required for each
POT pin.
This means you will probably not be able to filter them much. As you increase the capacitance you have to lower the maximum resistance and there's going to be a limit to how far you can change the values from the recommended ones.
I wrote a Breakout game for the Commodore VIC 20 that used the paddles, I remember having to do an averaging of the values. This was done in machine language (the whole game was).
The paddles on the Commodore computers were always a little bit jittery, but if you're trying to use your paddle on a commercial game and it's really bad then you may not have a good potentiometer, as any professionally written game would have smoothing in software.