You could try using soft pastel sticks, and then finishing with a spray sealer afterwards. Pastel sticks are not wet, so they won't cause that problem, and you can use your fingers to smooth the color into the smaller spaces.

You could try using soft pastel sticks, and then finishing with a spray sealer afterwards. Pastel sticks are not wet, so they won't cause that problem, and you can use your fingers to smooth the color into the smaller spaces. You could also use Q-tips or a toothpick to add pigment into the interior regions of the rose--but it would be difficult to make the coverage even.

Reading the post about airbrushing above sparked another idea that you could try. What about adding another layer of papier mache using colored tissue paper? It will still be very difficult to get color into the interior sections, but it could allow for some interesting layering of color for shadowing, etc.