Cellular base stations (BSs) powered by renewable energy like solar power have emerged as a promising solution to address the issues of reducing the carbon footprint of the telecom industry as well as the operational cost associated with powering the BSs. This paper considers a network of off-grid solar powered BSs and addresses two key challenges while operating them (a) avoiding energy outages and (b) ensuring reliable quality of service (in terms of the network latency). In order to do so, the problem of minimizing the network latency given the constrained energy availability at the BSs is formulated. Unlike existing literature which have addressed this problem using user-association reconfiguration or BS on/off strategies, we address the problem by proposing an intelligent algorithm for allocating the harvested green energy over time, and green energy and delay aware downlink power control and user association. Using a real BS deployment scenario, we show the efficacy of our methodology and demonstrate its superior performance compared to existing benchmarks.