Considering safety management systems are composed of a coal mine enterprise and a manager, incentive contracts for coal mine production are designed to improve the safety level of coal mine production. Managers must devote costly efforts in terms of both safety and production to increase the output of mines. Based on principal–agent theory, we designed an incentive contract considering moral hazard and a menu of contracts considering moral hazard and adverse selection. The results showed that when an enterprise cannot observe the manager’s efforts, the manager’s risk aversion reduces their production and safety efforts, and the enterprise needs to share its output risk with the manager. When the enterprise cannot observe the manager’s efforts and the cost type of the safety effort, a menu of contracts can be used to screen the manager’s cost type. However, high-cost contracts fail to motivate a high-cost manager and allow the high-cost manager to reduce safety and production efforts. A low-cost manager can obtain positive information rent from an enterprise without changing safety or production efforts. We provide some suggestions and references for the safety management of coal transportation in mines.