Are you saying you have sun only from noon to afternoon? If so, I don't think that's enough sun for peonies. Of course, you can always grow one and see how it does.

I've found peonies super easy to grow, just follow some good instruction online. I always plant in fall.
I have a lot of peonies (including the duchesse d. n. and
Mon. J.E. and Alex. Fleming - mine always flop no matter what the conditions - flowers are just too heavy for the stems. But for just one peony, it'd be super easy to use a peony support.
As to long bloom - all mine typically last a week, unless the weather is really stinky.
You probably want to stay away from single blooms. My single bloom "Dancing Butterflies" is pretty, but very short lasting blooms!!