This paper studies resource allocation for a fully sustainable cooperative network, which consists of multiple Internet of Things (IoT) nodes powered by radio-frequency (RF) energy, one relay with renewable energy supplies, and one destination. Specifically, the relay forwards the data received from IoT nodes to the destination and charges the IoT nodes at the same time. A throughput maximization problem is formulated, which takes into consideration the upper bound of transmit power, stochastic energy harvesting (EH) process and channel conditions. To solve the formulated problem, we analyze the time allocation for cooperative communications with EH, considering both data and energy dependency of the two hop transmissions in three cases with different parameters. Based on the analysis, we derive the closed-form solutions of optimal time and power allocation in a network with symmetric links. Extensive simulations validate the analysis and demonstrate the effectiveness of the proposed algorithm.