To achieve carbon peaking targets in China's agricultural sector, it is urgent to establish a scientifically sound and equity-efficiency-balanced allocation mechanism for agricultural carbon emission rights. This study proposes an integrated optimization framework that combines the autoregressive integrated moving average (ARIMA) model with the zero-sum gains directional distance function (ZSG-DDF) model. The framework aims to improve the allocation efficiency of agricultural carbon emission quotas among provinces under a fixed national emission cap. First, based on agricultural input–output data from 2005 to 2020, the ARIMA model is employed to forecast relevant indicators for 30 provinces. Taking into account China's national goal of reducing agricultural carbon intensity by 60% in 2030 compared to 2005, initial provincial-level carbon emission quotas are calculated accordingly. The ZSG-DDF model is then applied to evaluate the efficiency of these initial allocations. The results reveal that only 10 provinces—including Jiangsu, Fujian, and Guangdong—are on the DEA efficiency frontier, while the remaining provinces exhibit varying degrees of inefficiency. To address these disparities, a 19-round dynamic reallocation process is conducted using the ZSG-DDF model. During this iterative process, emission quotas are transferred from inefficient provinces to efficient ones, while maintaining the national carbon cap. Eventually, all provinces reach DEA efficiency. Specifically, provinces such as Shanxi and Xinjiang experience quota reductions, whereas Jiangsu and Guangdong receive additional quotas, forming an optimal allocation pattern characterized by a shift toward high-efficiency regions. Based on these findings, three policy recommendations are proposed: (1) establish region-specific carbon reduction targets; (2) design a performance-oriented dynamic quota adjustment mechanism; and (3) create a special fund to support the green transformation of agriculture. The proposed ARIMA–ZSG-DDF hybrid framework not only extends the predictive capability of traditional DEA models but also enables direct handling of undesirable outputs and total resource constraints. Furthermore, the model is highly adaptable across industries and administrative levels, and can be extended to carbon governance in other emission-constrained sectors such as industry and transportation, as well as at the county or municipal level. Overall, this study provides a quantitative decision-support tool and policy-oriented methodological innovation for designing agricultural carbon peaking pathways in China, contributing to the realization of carbon neutrality goals at the sectoral and regional scales.