We consider efficient scheduling for a delay constrained multi-rate CDMA system. We first find the optimum schedule for CDMA systems without transmit diversity (TD), that minimizes the average transmission energy per bit while maintaining the short term average throughput for each user in the system. We observe that the specifics of the scheduling problem enables it polynomially solvable. Next, we consider the case when mobile devices are capable of employing two antennas and use Alamouti scheme to achieve TD. We observe that our proposed scheduling protocol can be extended to the system with TD with a modest sacrifice in performance and significant saving 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 energy savings they provide with respect to the TDMA-type scheduling.