Peonies come in an array of Pinks, Coral, Yellow and White. They are showy, yet refined; feminine yet bold. They (like other strong flower presences, Orchids or Dahlias for example) can stand on their own or integrate nicely with other flowers.
They aren't an inexpensive flower. But since they have a larger flower head you can get away with including a few and still make a statement in an arrangement. If your budget is more robust, then by all means put as many luscious peonies together as you can!
I remember one wedding we decorated that was to be of all deep pink peonies. What a joy! I even liked seeing all of them in the flower buckets before they were arranged. It was just a lovely swath of multi-petaled color. Nothing could have been more basic and more purely beautiful.
Other than that Peonies aren't available year round, drawbacks in using them are few. Because of their size, applications Peonies aren't appropriate for are smaller pieces like boutonnières and corsages. Even using unopened buds is not so helpful in these cases. But, this dilemma can be easily solved.
If other flowers are being used in the event, then perhaps another “face” flower - a Rose or Mini Calla Lily - could be a nice alternative. I like to add additional elements like tiny flower buds, sprigs of greens or berries to add interest to these smaller pieces also. Sometimes I will use a cluster of flowers, like spray roses or florets from such as a Delphinium or Lisianthus. Another option, particularly if only Peonies are being used in the event, is an attractive combination of greens - perhaps with pods, grasses or berries incorporated. I then like to tie off the piece with a very thin ribbon that is color coordinated to the event.
Unfortunately Peonies aren't available year round. But when they are I believe it is hard to go wrong in using them in whatever capacity. And Peonies symbolize good health, prosperity and a promising marriage – so a perfect wedding flower!