Discount for products of specific categories

Log in your administrator panel and click on the Discounts and coupons link in the CATALOG side box on the left.
Open the Category discounts tab and create a discount using the Add new discount(s) form selecting Discount in the Type option.
Click on the details link of this discount.
Enter the desired value of the discount in the Value option, select the desired variant in the Type option.
Click on the Update button.
Select check boxes of the desired categories.
Click on the Update button.