Slings were actually used well into the medieval period in Europe, as well as the staff sling.
I have created a post where I suggested that a unit called the [Staff Slinger] could be added to the game. (The [Staff Slinger] a New Trainable Unit from the Siege Workshop)
From one of the responses that I got from my post, a user by the name of @PlumpDucklin suggested that the [Staff Slinger] unit could roughly cost: 50 Wood and 20 Stone, which would implement a special cost for this unit.
I am always open for feedback concerning this unit concept, so please share your thoughts about this unit idea in the post section that I have created.