My toddler goes through days, even a week here and there where she refuses to nap. Since my baby typically naps around the same time in the afternoon. I needed a quiet activity and I also wanted to make sure M stayed in her room.
If she is refusing to nap. I lay a blanket on the floor and let her pick a tote to play with. Sometimes, she picks two. I tell her she needs to stay in her room for quiet time and play with what is in the totes. It is a work in progress, of course. She is 28 months old. So, not yet 2 & 1/2. I just try to remain consistent with everything we do.
Thanks again to pintrest I discovered the world of quiet time totes. I find that people typically label them by day. I chose not to do that. M can pick the tote she wants to play with that day. I think that works best for her.