What's a good way to change the color of black (or gray or tan or blue) interior plastic into red interior plastic?

Spray-on SEM Vinyl Dye is your best bet.  It comes in a wide variety of standard colors, or can be computer matched and custom mixed at most automotive paint retailers.  I did a complete interior color change on an old F150 I had (went from red to blue) and it still looked as good when I sold the truck seven years later as it did the day I did it.  I used it on the door panels, headliner, dash, and sun visors and never experienced any deterioration, fading, or flaking.

Dwayne