Edge computing is a rapidly developing research area known for its ability to reduce latency and improve energy efficiency, and it also has a potential for green computing. Many geographically distributed edge servers are powered by renewable energy sources, due to the difficulties of using traditional power supplies or because of advancements in energy harvesting technologies. These green edge servers can cut down carbon emissions by processing tasks locally, but the inherent limitations of their computing capacity result in some tasks having to be uploaded to a data center to meet service-level agreement (SLA) requirements. To further reduce carbon emissions in cloud-edge systems, scheduling tasks to those low-carbon data centers while meeting latency constraints is highly beneficial. In this paper, we propose a low-carbon cloud-edge scheduling algorithm that utilizes Lyapunov optimization techniques and Markov approximation to address the long-term optimization problem of carbon emissions. Our algorithm guarantees provable performance, and simulation results demonstrate its effectiveness in striking a balance between carbon emissions and task latency.