Need to use product_id and not sku!  use sku to get item and then set product_id

one example of one item.

public string UpdateInventory(string sku, int inStock, string stkQty)
        {
            if (string.IsNullOrEmpty(this.SessionId))
                this.Login();

            try
            {
                string prodID = string.Empty ;
                catalogInventoryStockItemEntity ie = new catalogInventoryStockItemEntity();
               
                MagentoPushPullService.MagentoWebService.catalogInventoryStockItemUpdateEntity cisi = new catalogInventoryStockItemUpdateEntity();
                cisi.is_in_stock = inStock;
                cisi.qty = stkQty;
                cisi.is_in_stockSpecified = true;
               
// you can pass in more than one product at a time by setting/passing in an array of strings
                string[] item = new string[1] ;
                item[0] = sku;
               
                foreach (catalogInventoryStockItemEntity  sie in   magentoService.catalogInventoryStockItemList(this.SessionId,item))
                {
                    prodID = sie.product_id ;
                }

  // Update product by product id from StockItemList call
                int i;
                i = magentoService.catalogInventoryStockItemUpdate(this.SessionId, prodID, cisi);

                foreach (catalogInventoryStockItemEntity sie in magentoService.catalogInventoryStockItemList(this.SessionId, item))
                {
                    string tmp = sie.is_in_stock;
                }

              
                return "Success";
            }
            catch (Exception ex)
            {
                //TODO: Log the error               
                return "Error updating inventory";
            }
          
        }