Yes goats cheese can give some people diarrhea especially if the person has a goat cheese intolerance.
You could also experience other digestive issues such as stomach pain, bloating etc.
Diarrhea from goats cheese is also possible if you eat too much goats cheese although when you get diarrhea from goats cheese you might have an intolerance to the goats cheese and should see a doctor if the diarrhea happens every time you eat the goats cheese.
You could also be lactose intolerance which causes the diarrhea from the goats cheese and the Lactase is an enzyme in the small intestine which breaks down the sugar in the dairy products that you eat and when you have Lactose Intolerance that sugar cannot be broken down properly which makes it hard to digest milk products and dairy products.
So you might have a lactose intolerance to the goats cheese.