Maybe you could transition it away from "nap time" to just "quiet time". Having quiet time during the day is a good thing - it teaches children that everything doesn't have to be go-go-go and they don't have to be entertained all the time. It also teaches them essential skills they'll need later in life - like how to relax and slow down.
When I was young, we used to have "turtle time" (I think it was called this because we were quiet and slow, like a turtle. We even did it during Girl Scout camp-outs). It was an hour or so in the middle of the afternoon when we spent some quiet time alone in our rooms. We could nap if we wanted, but otherwise we could read, color, or play quietly. As I got older, I started missing that time to wind down and relax. I try to have that time even now that I'm an adult.