Quiet time can include playing peacefully or looking at books:
"As for napping, hang in there, it may be a phase. I thought my daughter was totally done with naps (she was never a big napper), but she's suddenly a total sleepyhead and back to napping every day without a struggle. I found even when she wasn't napping I'd implement "quiet time". She didn't have to sleep but had to sit in her room and look at books or play quietly. She seemed to like the time alone; she would sometimes be in there for 40 minutes. It helps a bit, and I think it was the enforced quiet time without the pressure of sleep that has made napping easier for her now."
Give them a few toys and books in theird bed:
"My son is going to be three at the end of August, and we've been struggling with this since he was 2.5. My pediatrician had wonderful advice, which has worked--quiet time should be non-negotiable. Children need to learn how to play on their own and need some downtime. Make naptime fun to the extent possible. Let them put a few toys/books on their bed and, after 20-30 minutes of playing on their own, let them out. If he won't stay in the room alone, stay with him in the beginning. But don't talk to him. Instead, bring a good book and tell him that it's quiet time and that he should read/play on his bed. It has worked very well. He has now picked a nap back up again and sometimes will take one and sometimes not. I was panicking at the thought of his not taking them, but the upside is that bedtime is earlier."
Contain the space:
"My son at 2.5 just wouldn't take his nap for a while. I told him it was up to him to sleep or not but that he had to stay in his room (preferably in his bed) and play/read quietly during naptime. He tried to get out of his room several times, but I would bring him back in every time, and tell him to stay there. He cried a little bit but got it very quickly, and in the end liked his time alone. If you are afraid that he will walk out of his room, you can put a gate right outside his room (we were ready to do it when he finally stopped walking out) so that, even if he opens the door, he can't go anywhere. The good news is, he went back to napping relatively quickly, even if after that he was always "reading"/playing for a while before falling asleep. And I had this time for myself again!"