Incorporating cognitive radio in traditional wireless sensor networks creates a new Internet of Things paradigm, which is termed as cognitive radio sensor networks (CRSNs). This paper proposes a novel stability-aware cluster-based routing (SACR) protocol for CRSNs. The major innovation of SACR lies in the seamless integration of opportunistic forwarding and a stable clustered architecture. In the aspect of cluster formation, we propose to take into consideration of spectrum dynamics and energy consumption in the clustering process. The resulting clustered architecture is stable and thus avoids large communication overhead due to high clustering frequency. For data routing, SACR adopts an opportunistic forwarding scheme which selects a unique cluster head by accounting for its cluster size, number of available channels, and hop distance to the gateway. Last but not least, SACR is a distributed routing protocol that does not require a dedicated common control channel. Simulation results show that SACR outperforms existing routing protocols for CRSNs in terms of packet delivery ratio, delay, energy consumption and signaling overhead.