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Delay-tolerant networking (DTN) offers a novel architecture that can be used to enhance store-carry-forward routing in satellite networks. Since these networks can take advantage of scheduled contact plans, distributed algorithms like the Contact Graph Routing (CGR) can be utilized to optimize data delivery performance. However, despite the numerous improvements made to CGR, there is a lack of proposals to prioritize traffic with distinct quality of service (QoS) requirements. This study presents adaptations to CGR to improve QoScompliant delivery ratio when transmitting traffic with different latency constraints, along with an integer linear programming optimization model that serves as a performance upper bound. The extensive results obtained by simulating different scenarios show that the proposed algorithms can effectively improve the delivery ratio and energy efficiency while meeting latency constraints.