I can't believe I have a 26th month old that won't nap, but I do. We've instituted quiet time over the past month which sometimes turns into a nap if he is sick or exhausted because it is VERY similar to our napping routine.
First, semantics. I made it VERY clear that he didn't have to nap. We were getting into bed for quiet time and to rest our bodies.
We still bring our bottle of milk (yes, my child is old enough to drop naps but still need a bottle... shoot me now!

), still read 5 stories. Then, I tell him that *I* have to rest my eyes, or do my knitting work, or do the dishes, etc. (The first two I did a lot when we first started so I could monitor the quiet time. Now I tend to make up a task like dishes or laundry or something.) I remind him that he is free to read any of the additional books we have on the bed and play with his stuffed animals, but he must stay on the bed until X:XX time. He is very good with numbers, so that usually does it for us.
One thing about this age is being realistic about the length of the quiet time. I find I can get 30-40 minutes (plus the 15 minutes of wind down with his stories) but no more. Also, in the beginning, I did set a timer for 30 minutes telling him that mama needed to rest her eyes until the bell went off. I think it helped him learn internally what 30 minutes of quiet meant.
The other thing is that my kid could not just play in his room with toys without my help for 40 minutes. Limiting movement is a huge deal since we've mostly co-slept and we've never done a crib or even a shut door routine. But it is the only way I can make sure he slows down enough to get rest (which he does still need, even if he doesn't need sleep) and for me to get a few minutes to myself.