This paper considers a cooperative Internet of Things (IoT) system with a source aiming to transmit randomly generated status updates to a designated destination as timely as possible under the help of a relay. We adopt a recently proposed concept, the age of information (AoI), to characterize the timeliness of the status updates. In the considered system, delivering the status updates via the one-hop direct link will have a shorter transmission time at the cost of incurring a higher error probability, while the delivery of status updates through the two-hop relay link could be more reliable at the cost of suffering longer transmission time. Thus, it is important to design the relaying protocol of the considered system for optimizing the information freshness. Considering the limited capabilities of IoT devices, we propose two low-complexity age-oriented relaying (AoR) protocols, i.e., the source-prioritized AoR (SP-AoR) protocol and the relay-prioritized AoR (RP-AoR) protocol, to reduce the AoI of the considered system. By carefully analyzing the evolution of the instantaneous AoI, we derive closed-form expressions of the average AoI for both proposed AoR protocols. We further optimize the generation probability of the status updates at the source in both protocols. Simulation results validate our theoretical analysis, and demonstrate that the two proposed protocols outperform each other under various system parameters. Moreover, the protocol with better performance can achieve near-optimal performance compared with the optimal scheduling policy attained by applying the Markov decision process (MDP) tool.