I'm looking for help/ideas on this one too . . .
My dd doesn't always nap and when it's clear she's not going to sleep, I tell her we can go downstairs and have quiet time (while her twin brother sleeps).
She usually plays pretty well for awhile (since she's not being actively annoyed by her brother), and I will suggest things, like puzzles, or would she like to make a snack for bear (in the play kitchen), take doll for a walk (in a push toy we have), etc.
I'm not "allowed" to read (she sees that as an invitation to read to her), but I do try and knit or do something with my hands. I will engage with her when she seems to need it, but then remind her that I need quiet time too and would she like to try (whatever other thing I can think of).
It goes okay, but I am DREADING her brother giving up his nap, b/c he definately will not "get" the idea of quiet time.