Recent work in fair machine learning has proposed dozens of technical definitions of algorithmic fairness and methods for enforcing these definitions. However, we still lack an understanding of how to develop machine learning systems with fairness criteria that reflect relevant stakeholders' nuanced viewpoints in real-world contexts. To address this gap, we propose a framework for eliciting stakeholders' subjective fairness notions. Combining a user interface that allows stakeholders to examine the data and the algorithm's predictions with an interview protocol to probe stakeholders' thoughts while they are interacting with the interface, we can identify stakeholders' fairness beliefs and principles. We conduct a user study to evaluate our framework in the setting of a child maltreatment predictive system. Our evaluations show that the framework allows stakeholders to comprehensively convey their fairness viewpoints. We also discuss how our results can inform the design of predictive systems.