One option is to find case studies that involve root cause analysis for the core problem/opportunity facing an organization. Several of the ones offered by Harvard or other business schools would fit the bill (http://hbsp.harvard.edu/product/cases). The person with the teacher's guide would be the sounding board to have the BAs ask more questions.

Alternatively, you could look for movies that have deep characters and have the BAs try and understand the motivation behind certain actions seeing only certain clips of the movie (provided the movie reveals the character's motivation later on). Have them ask you questions to see if they can find out why they perform a certain behaviour.

Pick a news article and have them debate the causes of a current issue (war, politics, local civic challenges, etc.). Newspaper articles almost never provide full background or a deep understanding of an issue - get them to figure out what other information they need in order to better understand the problem. 

Jarett