Looking for help with particle colors filling a shape

Hello all: I have created a particle system that is emitting randomly placed particles inside of a spherical shape. Each particle lives for only 2 frames giving the effect of a series of flashes filling a spherical volume. Imagine a bunch of fireflies blinking inside of a transparent ball.

However, given what I'm designing, I need for there to be no particles emitted very near the center of the sphere or if they are emitted they need to be black so that they don't show up.

Is there a way to control the particle color so that this can be accomplished without having to deal with modeling strange shapes such as a sphere within a sphere with the inner sphere connected to the outside?