Government regulation and financial pressure are real challenges that firms have to face in reducing emissions. This study constructs a supply chain composed of a retailer and a capital-constrained manufacturer, and where the manufacturer is regulated by a carbon cap-and-trade policy. On this basis, this study develops three analytical models integrating external financial support: manufacturer independent abatement, supply chain loose co-operation for abatement, and energy service companies providing abatement services. Subsequently, the study explores manufacturers’ choices of abatement models and supply chain members’ operational decisions under these models. Furthermore, the extension of this study delves into a scenario in which supply chain members closely collaborate to collectively reduce emissions, while also introducing a contract as a coordination mechanism. The results demonstrate that: i) When the interest rate exceeds the corresponding threshold, the profit of the manufacturer under the energy service company abatement model exceeds that of the loose cooperation and independent abatement models. ii) The financial strain on the manufacturer under the energy service company abatement model is inversely related to carbon prices and positively associated with the abatement efficiency of the energy service company. iii) In the energy service company abatement model, if the revenue sharing ratio is below the corresponding threshold, the profits of both the manufacturer and the retailer show a positive correlation with this ratio. iv) The two-part tariff contract developed in this study allows the unit abatement level and firm profits in independent abatement to align with those in closely cooperative abatement.