We consider efficient scheduling for a delay constrained CDMA Wireless Sensor Network (WSN). Given a twotiered WSN model, we first find the optimum schedule for the intra-cluster communications, that minimizes the total transmit power of the sensor nodes, while maintaining the short term average throughput at each sensor. We show that the specifics of the scheduling problem enables it polynomially solvable. Next, We consider the inter-cluster communications where cluster heads are capable of employing two antennas and use Alamouti scheme to achieve the transmit diversity (TD). We observe that our proposed scheduling protocol applied to the intercluster communications provides a near-optimum solution, with a modest sacrifice in performance and significant savings in computational complexity as compared to the optimum scheduler. Simulation results are presented to demonstrate the performance of the proposed scheduling protocols, and the considerable power savings they provide with respect to the TDMA-type scheduling.