Then you could put the capacitors across the LEDs, on the other side of the resistors. Or were you thinking of using resistors? I could see a switched current regulator.

 

Well, see the attached.

It's a somewhat crude attempt at using a comparator and some discrete components to emulate a "buck" DC-DC converter.

R1 keeps the gate of Q1, a P-ch MOSFET, held at the source potential to keep it turned off by default. D1 is a 10v Zener, which limits Vgs to -10v when current is being sunk through R3/Q2.

If the voltage across R4/D2 (the OP's simulated LED) drops below the threshold (set by R6 & R7) then Q1 is turned on, and current flows through L1, charging the cap and providing current to the simulated LED. When the threshold is exceeded, Q2 is turned OFF, so R1 pulls the gate of Q1 high, cutting off the current to L1. R7 provides hysteresis to keep the output of U1 from cycling too quickly or triggering from noise.

Since the current from Q1 is turned off, L1's ends swap polarity. D3 provides a path to ground, keeping the current flowing into C1, that capacitor you really wanted to have in there.

This isn't a switching current controller; it's a switching DC-DC "Buck" converter.

Ideal regulated voltage sources have zero output impedance.
Ideal regulated current sources have infinite output impedance.
Since an ideal capacitor has zero output impedance, it doesn't fit into the regulated current model. Unless, of course, you want to change an ideal current source into a much less than ideal current source.

But, such a circuit would be made a lot more efficient and much more simple by using something like Linear Technology's LT1111, which is a fixed DC-DC buck converter IC in 8-pin DIP form; it only requires a few external components.
http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail?name=LT1111CN8-12-ND