Green contracting mechanisms are utilized to integrate sustainable and environmentally protective goals into business objectives. This study proposes a framework for the design of green contract mechanisms in forestry supply chain management. We assumed that there was an applicant for harvesting timber in a forest, and that the owner tried to evaluate different scenarios to design a green contracting mechanism. We also assumed that the owner of a forest cared about green goals, such as carbon dioxide absorption, in the forest. We regarded the interests of the parties, such as the profit of the applicant as well as the green goals of the forest owner. We used multi-attribute decision-making techniques such as the weighted sum, normalized weighted sum, TOPSIS, and VIKOR to evaluate the various scenarios. In the literature, another approach was taken to solve a similar problem based on multi-objective techniques and the Pareto optimality concept. We compared the outcomes of the determined framework with the outputs of the previously employed methods. The recommended framework can provide more interpretable results since it considers the interests of different sides. The framework can assist businesses in designing contracts that promote sustainable operations and support compliance with the United Nations’ Sustainable Development Goals.