Previous literature has proposed that international cooperation in small groups of countries, so-called “climate clubs,” will be an effective complement to the UNFCCC process. Little research has investigated the potential for an industry-specific climate club. Filling this gap, we assess possibilities for a climate club in the aviation sector in which “leader” countries pay followers to use sustainable aviation fuels (SAFs). We seek to understand if such cooperation is possible at a reasonable price. In addition, we examine the ideal coalition size for successful cooperation and the sensitivity of outcomes to SAF price and mix rate. To investigate these questions, we use an agent-based model calibrated with data on countries’ populations, GDP, and jet fuel consumption. Our results indicate that modest cooperation is possible under various circumstances but limited by SAF price and maximum mix rate. Furthermore, there may be compelling reasons to start with a very small number of club members.