So, you are rendering the basic particle system (non-nParticle), and you are using the sphere render type? What you want to do is add a dynamic property on the particle shape node. With this added property, you can either right click the blank spot, and add a ramp based on the age of the particle, or you can write your own expression to color the particles.
(The attribute you have to add is RGB per particle)
If you'd like to write your own expression to color the particles, you can mess with a few of these statements:
particleShape1.RGBPP = <>;
You would want to make this expression kick in at creation time, to generate a random color.
This expression pretty much defines the R G and B attributes of the per particle attribute, as random numbers between 0 and 1.
If you could, please give me some more information regarding your issue.
Regards,
Kyle