When i put cow milk in my coffee, i have no problem. however, when i use it with cereals, i have diarrhea the next day. do i have lactose intolerance?

Probably yes: It may be the amount. Usually people use more milk in their cereal than the amount they use in their coffee.

Quantity dependant: You may since the quantity of milk you use in cereal is likely many times more than in coffee. Lactose intolerance is the inability to break down the complex sugar, lactase, into absorbable simple sugars. Therefore symptoms are often quantity dependant. Try using a lactose predigested milk.