I have to agree with Arlene (Pirl) that clematis blooming time is rather unpredictable. Some years, they will bloom with the peonies and some years they bloom later or earlier than the peonies. Having said that, the few that have bloomed somewhat consistently with the peonies in my garden are Arabella, Little Duckling, Diana's Delight, and Sarafina. Pink Champagne is another possible good one that blooms at the same time of peonies if you don't prune it.
Here is a pic of Sarafina. I was hoping that it would bloom at the same time as my lavender pink NOID tree peony but as you can see the TP had already finished blooming just when Sarafina was at its peak. It kinda clashed with the coral color of Coral Charm. I am planning to move this clematis to accompany Cora Louise. I think they will look swell together if it can consistently bloom at the same time as CL blooms.
Sandra Marie with Little Duckling clematis
Magical Mystery Tour with Arabella
Diana's Delight is a good clematis to accompany late blooming whites.
Walker's low is a great companion plant for peony but it looks shabby after the first bloom is done.
You kind of have to experiment to see what works best. Sometimes the result is not quite as what you expect if the bloomings do not coincide. Anyway, I think that is what gardening is so much fun. You can be wrong but the flowers still look good no matter what you pair them with.