Hi Michael, I have a few primroses in the back yard near some peonies, The primroses are closer to the house so are shaded quite a bit more than the peonies but they bloom at the same time. You can also do early blooming lilies and daylilies. Irises bloom at the same time and look pretty. I like the different shape of the strappy leaves compared to the peony shrub. Rocky Mountain Penstemon might be the wrong color for you (blue/purple), as is false indigo, but blooms at the same time, too. Different varieties of those families bloom different colors, salmon pink, pink, yellow or white, very pretty together.
I have very early to very late peonies here, start blooming mid June and finish mid-late July with our micro-climate locally. Most daylilies and all of the late lilies bloom well after the peonies are done. Elevated pots of morning glories work well to keep the blooms going, just have to be pretty vigilant the next spring to get rid of the volunteer plants so they don't choke out any other plants. Just a few ideas!