Autonomous Driving System (ADS) testing is essential to ensure the safety and reliability of autonomous vehicles (AVs) before deployment. However, existing techniques primarily focus on evaluating ADS functionalities in single-AV settings. As ADSs are increasingly deployed in multi-AV traffic, it becomes crucial to assess their cooperative performance, particularly regarding deadlocks, a fundamental coordination failure in which multiple AVs enter a circular waiting state indefinitely, resulting in motion planning failures. Despite its importance, the cooperative capability of ADSs to prevent deadlocks remains insufficiently underexplored. To address this gap, we propose the first dedicated Spatio-Temporal Conflict-Guided Deadlock Avoidance Testing technique, STCLocker, for generating DeadLock Scenarios (DLSs), where a group of AVs controlled by the ADS under test are in a circular wait state. STCLocker consists of three key components: Deadlock Oracle, Conflict Feedback, and Conflict-aware Scenario Generation. Deadlock Oracle provides a reliable black-box mechanism for detecting deadlock cycles among multiple AVs within a given scenario. Conflict Feedback and Conflict-aware Scenario Generation collaborate to actively guide AVs into simultaneous competition over spatial conflict resources (i.e., shared passing regions) and temporal competitive behaviors (i.e., reaching the conflict region at the same time), thereby increasing the effectiveness of generating conflict-prone deadlocks. We evaluate STCLocker on two types of ADSs: Roach, an end-to-end ADS, and OpenCDA, a module-based ADS supporting cooperative communication. Experimental results show that, on average, STCLocker generates more DLS than the best-performing baseline.