D.P.
Hi M.,
I too have a 3-1/2 year old son who is beginning to not take naps in the afternoon. He is ADHD, so getting him to have quiet time is sometimes difficult.
What I do is after he has lunch, I put him in his bed. He does have stuffed animals in his bed and is allowed to take one additional toy to bed with him. He usually takes one of his Thomas Trains with him and that is fine. If he wants a book, I'm okay with that as well, but that doesn't typically happen with my son.
If I haven't heard any movement after about a 1/2 hour, I go and check on him. More times than not, he is napping. However, there are those days that he doesn't. When I put him down, I do tell him that he is not allowed to get out of his bed until I come and get him. He does listen and will call for me if he wants to get up.
If it's just quiet time and no napping, if he's not causing any issues and playing quietly in his bed, I usually come back after about an hour and allow him to get out of his bed. That gives me enough time to get a load of laundry switched out or dishes done and house quickly picked up before he comes out.
Hope that helps a little! Good luck!
D.