Documentation on Show says "Options explicitly specified in Show override those included in the graphics expression" so I hoped that something like

Show[{p1,p2}, PlotStyle->{Red,Green}]

would work. But it doesn't. I think it would be very useful to be able to combine previously generated graphics in a single plot as you want. Particularly since we would be able to do the basic work without worrying about setting things up for later display. But I don't know how to do this -- maybe others will comment?

Thanks for trying to help, but this isn't my situation. Let me be more explicit:

gr1=ListPlot@elaborate calculation .... which take several minutes and I don't want to run it again

gr2=ListPlot@ another elaborate calculation .... which take several minutes and I don't want to run it again

When I made gr1 and gr2, I did't plan on showing them together, so I didn't do anything special about the colors. Now I want to put them together, and have gr1 in one color and gr2 in another color. Sop I want to do something like

I should also mention that the grouping I used above is not necessary. I often produce that in building the graphic list, but it is only the order that matters.

Graphics[{Blue, Disk[{-1, -1}, 1], Disk[{0, 0}, .5], Yellow, 
  Disk[{1, 1}, 1]}]