Internal Resistances of Capacitors
The ideal capacitor has no resistance either in series or in parallel with it.  What you are therefore asking about is non-ideal behavior.

Truly modeling all the non-ideal characteristics of any real part is impossible.  Everything has some series inductance, some series resistance, some leakage resistance, and some parasitic capacitance.  Then the extra resistances, capacitances, and inductances of the model each have their own non-ideal characteristics.  This mess blows up exponentially, and has to be carried out a infinite number of levels to get to reality.

So what you are really asking is whether there are two resistances in some simplified model of a non-ideal capacitor.  There certainly can be, depeding on what you consider simple versus useful enough.

If you start out saying you only want to model the non-ideal characteristics of a capacitor with two resistances, then the obvious choice for those would be the equivalent series resistance (ESR), and the leakage resistance.

The ESR can be a few m&Omega; or even less (eventually the equivalent series inductance dominates) for small ceramic caps, up to a few Ohms for large electrolytic caps.

The leakage resistance accounts for the reality that the insulation used to make the capacitor isn't perfect.  Even glass or other ceramics will allow a little charge to trickle thru with applied voltage.  This is the reason that caps self-discharge.  Air-plate capacitors come about as close as possible to no leakage (very high effective leakage resistance).  However, something has to eventually hold the plates in place, so there is always some leakage path thru solid material.