At different locations, I've had apples, plums, apricots and cherries.
Not in one dedicated run... but in different paddocks that were open to the
chickens.
All of these trees did quite well.
I have never tried mulberries, but from what I understand this is a near perfect match.
The trees benefit from the chickens eating pests and bugs below the tree.
The chickens benefit from a diet of fallen mullberries for most of the summer.