The Parrot tulips are gorgeous! This is the 1st year that I've not planted them. Unfortunately, they have never returned for me, and I've had to replant them every year. I agree with Karen, the Darwin hybrids, and single late tulips do return for me.
Our tulips bloom here well before the peonies are ready to bloom. What blooms at the same time as the peonies here are bearded and Siberian irises, and clematis.
Here's a pic of Wladyslawa and Misaka with a bearded iris, and clematis Arabella to the left and Multiblue in the back.
