Evaluating the degree of coordination among regional carbon emission systems is key to achieving an earlier carbon peak and carbon neutrality. However, quantifying the co-evolution of carbon emissions among regions is challenging. Therefore, we propose a data-driven method for evaluating the synergetic development of the regional carbon emission composite system. First, the proposed method employs relevant data to calculate the carbon emissions and carbon emission intensity of each subsystem within the region to describe the temporal trends. The inverse entropy weight method is then used to assign weight to each order parameter of the subsystem for data processing. Then, we perform synergetic development assessment of the composite system to measure the order degree of each subsystem, the degree of synergy among subsystems, and the overall synergetic degree of the temporal evolution of carbon emissions between regions. Finally, the evaluation results can be used to suggest measures for the regional coordinated reduction of carbon emissions. In this study, we used data from the Yangtze River Delta (YRD) region from 2010 to 2019 to demonstrate the feasibility and effectiveness of the method. The results show that there is still a long way to go to reduce carbon emissions in the Yangtze River Delta region. Economic development still relies heavily on fossil energy consumption, and the regional carbon emission reduction synergy is not high. This study provides theoretical and methodological support for regional carbon emission reduction. Moreover, the proposed method can be applied to other regions to explore low-carbon and sustainable development options.