I always napped alongside my kids. Both outgrew the need to nap at about 3.5 yo, by not falling asleep during the time we were lying down together. So I offered books and told them they could either sleep or quietly read. Sometimes they would read themselves to sleep, but usually not. Now at ages 4 (almost) and 6, we still have what we call "resting time" where we all lie down and read for an hour. (But I am the only one who often falls asleep!) On days when we are out in the afternoon, we skip "resting" and they are excited because they think they are getting away with something! But we always go back to it the next day, and often, even after I tell them an hour is up, they continue to read for quite a while!
Oh, and I forgot to mention, that having that hour of quiet time makes all the difference in their evening behavior. They end up quite refreshed, and go to bed on time (usually).