...one method might be to begin with a radial filled circle, black to white, in an RGB document, that way you can utilise the effects > photoshop effects options...
...and eventually ending up with a black 1bit bitmap noise object that can be colorised to any color, sat on top of a solid color...
...this will take some experimenting in illustrator, but is achievable...
...this method does result in a pixel 1bit bitmap image for the noise, but still good for high end print output, so long as resolution is taken into account...
...so before embarking on instructions, is the noise effect needing to be vector too, as this would make it a tad trickier? In which case you may have to implement the live trace feature...
...by the time you got through that you may find it more efficient to create a dissolve in photoshop that you can import as a 1bit bitmap to illustrator to colorise...
Andrew