I wonder what reasoning your coach uses for not allowing a change-up. You mentioned a "rainbow", and that may indicate that your change-up is easy to sit on and hit. I would video tape yourself and see if you are "telegraphing" the change, in other words, throwing with a different arm speed or general set up. When throwing that change, everything should tell the hitter "fastball".
Furthermore, I disagree with those who would recommend that you throw it when your coach specifically tells you not to. That is, if you want to keep pitching. You may be ultimately responsible for how the pitch turns out, but its your coach who determines who plays and who sits.
Talk to him and get his input. Tell him you really want to learn to change speeds to screw up the hitter's timing, and enlist the coaches help in doing it successfully. Ask him how to do it and what to work on, then go home and do it. Next practice, bring it out and show the coach what you've accomplished in your own time, and see how willing he is to help you become a better pitcher!