Bought this Peony about 2 weeks ago, was happy and green with two buds at the time. Repotted in its own soil when we got it home, it gets quite a lot of sun and we have had several wet days recently. In the last week however one side has turned purple/brown and the bud has failed to open whilst the other side seems happy! Total novice gardener. Thanks for your help.
I would guess this was grown by the suppliers as a large plant (with maybe 20 or 30 stems and flowers) and then divided into the miserable looking thing you bought, to make more money selling them individually.
Splitting up the roots of large peonies is the normal way to propagate them, but it is best done when the foliage has died down for winter, not when they are in flower!
One of the two stems you bought was probably damaged when the original plant was split up, or you damaged it when you repotted it, and it is now pretty much dead.
Peony plants are notorious for not being able to support the weight of their flowers without supports, which may be how yours got damaged. I would put a stake in the pot and tie something loosely round the "good" stem before it also gets broken by the weather or the weight of the flower.
Since all the foliage dies every winter, the best way to buy peonies is as "bare root" plants in spring, like this video https://youtu.be/qb8ZJaFpFJw, not as fully grown potted plants in summer.
If what is left of your plant survives for the rest of the year, it will probably look better next year, but since it is small plant you may not get any flowers at all until 2021. But you know what the flowers will be like when it does get big enough to flower again, so don't get impatient and throw it out!