Of my two daughters, now both older, one would never take a nap. She may of had one or two afternoon naps her entire life. She is still a whirlwind of activity, loves her picture being taken, enjoys shows, live music, clubbing, in fact just about any activity that keeps her awake when the rest of us want to take a nap, nothing has changed.
My other daughter would sometimes take a nap if I did too. It would take me about 2 minutes to drop off. About half the time she would climb off the end of the bed and keep herself entertained playing quietly until I woke up. I was obviously tired, so she did not want to disturb me.
I am not sure that a single solution exists to your problem. I am sure that you know more about your child than any of us here.
Good luck, Agantum.