Linear regulator that regulates even with negative current?
VTT regulator, aka "DDR termination regulator".


PC motherboards use DDR busses which are transmission lines terminated by resistors to a certain voltage, which is managed by a "VTT regulator" which is able to sink or source current. The interesting bits here are the fact that motherboards are high volume, therefore many chips are available to do this job at cheap prices. Try googling the terms above, or using the search feature on digikey, looking for "termination regulator".


Opamp designed for capacitive loads.


Opamps usually dislike capacitive loads (due to phase margin issues) but there are ways around this. Some opamps are rebellious and will drive "unlimited capacitive loads" which are terms you should search. There are a few candidates.


Brute Force


If the max current the regulator will have to sink is known, a simple linear voltage regulator and a resistor sinking the max current will do the job. It is quite inefficient.


Roll your own


Most LDOs are voltage controlled current sources. The error voltage (output voltage minus reference) goes into a transconductance amp which creates a proportional current, and the output cap integrates this current and acts as a dominant pole for loop compensation. You can implement this yourself if you want, it isn't difficult.

If you want to create a voltage regulator which will work well with a known capacitance at the output, all you have to do is consider the output cap's ESR and capacitance, and create a circuit which synthetizes an impedance which is equivalent to some inductance and enough resistance in series to make sure the resulting circuit is nicely damped. This can be implemented with an opamp and some R/C in the feedback network, for example.