Recent advances in multi-agent reinforcement learning (MARL) allow agents to coordinate their behaviors in complex environments. However, common MARL algorithms still suffer from scalability and sparse reward issues. One promising approach to resolving them is automatic curriculum learning (ACL). ACL involves a student (curriculum learner) training on tasks of increasing difficulty controlled by a teacher (curriculum generator). Despite its success, ACL's applicability is limited by (1) the lack of a general student framework for dealing with the varying number of agents across tasks and the sparse reward problem, and (2) the non-stationarity of the teacher's task due to ever-changing student strategies. As a remedy for ACL, we introduce a novel automatic curriculum learning framework, Skilled Population Curriculum (SPC), which adapts curriculum learning to multi-agent coordination. Specifically, we endow the student with population-invariant communication and a hierarchical skill set, allowing it to learn cooperation and behavior skills from distinct tasks with varying numbers of agents. In addition, we model the teacher as a contextual bandit conditioned by student policies, enabling a team of agents to change its size while still retaining previously acquired skills. We also analyze the inherent non-stationarity of this multi-agent automatic curriculum teaching problem and provide a corresponding regret bound. Empirical results show that our method improves the performance, scalability and sample efficiency in several MARL environments.