Take this with a grain of salt, but when talking about a headphone amp:
Bright = my headphones need more current than this puppy can deliver
Dark = my headphones have too stiff membranes for this puppy to drive
Mid-centric = Bright + Dark
In other words, these impressions describe the behavior of the amp-headphone tandem, not the amp alone. If you look at the frequency response characteristics of amps, they are uniformly flat, i.e. with variations of 0.5 dB or better across the entire frequency range - this is hardly audible. So why do we hear them differently?
The answer is: the frequency response tests are performed on a specific impedance load (which is hardly ever specified), while your headphones most likely will have different impedance value. Moreover - if you check some of the headphone characteristics, you'll notice that their impedance changes depending on the frequency of signal. In practical terms it rarely matters as most of us don't spend hours listening to perfect single frequency sine waves, but that should give you some idea about the complexity of the interaction between the two. On top of that you have frequency dependent phase shifts, harmonic distortions etc - this all has impact on our perception of sound.
Coming back to your original question: looks like you are after an equalizer, not an amp
