This article 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. Specifically, in the SP-AoR protocol, the relay opportunistically replaces the source to retransmit the successfully received status updates that have not been correctly delivered to the destination, but the retransmission at the relay can be preempted by the arrival of a new status update at the source. Differently, in the RP-AoR protocol, once the relay replaces the source to retransmit the status updates that have not been successfully received by the destination, the retransmission at the relay will not be preempted by new status update arrivals at the source. By carefully analyzing the evolution of the instantaneous AoI, we derive closed-form expressions of the average AoI for both the 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.