Assuming by "negative dispersion" you mean that lower frequencies travel faster, don't try to invert the phase, this will be like trying to have a time-traveling dispersion filter. Rather, design an allpass filter with phase delay that increases (rather than decreases) with frequency.
If you're doing a 1st-order allpass, for example,
D1(z) = (-0.9 + z^-1)/(1 - 0.9z^-1)
will have a phase delay that decreaes with frequency. And
D2(z) = (0.9 + z^-1)/(1 + 0.9z^-1)
will have a phase delay that increases with frequency.
The only real drawback is you can't as cheaply or easily get comparatively large phase delays at higher frequencies.