It is anticipated that future wireless networks will make use of more renewable energy sources, e.g., solar, wind, and hydro, etc., in order to sustain the ever-growing traffic demands, while mitigating the effects of increased energy consumption. The most critical issue of developing a sustainable communications network is how to cost-effectively deploy access points (APs) with sustainable energy supplies and allocate network resources to meet the quality of service (QoS) requirements of users. In this paper, the traditional AP placement problem is revisited with sustainable power supplies. First, a constrained AP placement optimization problem is formulated. The objective is to determine the optimal placement of APs on a set of candidate locations such that the number of APs is minimized, subject to the constraints that QoS requirements of users can be fulfilled with the harvested energy. To further improve the sustainable network performance, joint power control and rate adaptation at APs is considered, based on different user demands and charging capabilities of the APs. After that, an efficient heuristic algorithm with polynomial time complexity is proposed. Extensive simulation results show that the proposed algorithm approaches the optimal solution under a variety of network settings with significantly reduced time complexity.