Which runtime?

draw order is usually just a slot array (.drawOrder) in the Skeleton object.
If you change the order of the contents of the array, you change the order the slots are drawn. First ones are under, last ones are on top.

In Unity?
Can you give an example how to change the order of an specific slot?

I think this method will work.

/// <summary>
/// Moves a given slot in the drawOrder. drawOrderOffset is the number of places to move the slot in the draw order. Positive values means the slot is drawn later.
/// </summary>
public static void MoveDrawOrder (Skeleton skeleton, string slotName, int drawOrderOffset) {
   Slot slot = skeleton.FindSlot(slotName);
   if (slot == null) return; // Do nothing if slot is not found.
   var drawOrder = skeleton.DrawOrder;

   int oldIndex = drawOrder.IndexOf(slot);
   int newIndex = oldIndex + drawOrderOffset;
   if (newIndex < 0) {
      newIndex = 0;
   } else if (newIndex > drawOrder.Count - 1) {
      newIndex = drawOrder.Count - 1;
   }

   drawOrder.RemoveAt(oldIndex);
   drawOrder.Insert(newIndex, slot);
}

Thanks Pharan! =)

Bump!

Leaving a comment here because thanks for that snippit of code, Pharan!