Multi-task allocation in multi-agent systems aims to accomplish tasks efficiently and successfully, while obtaining more rewards to enhance the entire system operation at the same time. Most existing assignment methods are based on agent coalitions, which cannot balance the profit distribution and task execution success rate or ignore the coalition stability, leading to a low execution level and assignment failures. Few coalition scheduling methods exist for multi-task allocation based on a fixed agent population. In this paper, we propose an effective stability quantum particle swarm optimization (SQPSO) algorithm which includes high rewards obtaining, benefit dividing, coalition stability insuring, and a historical task mechanism for search acceleration. Secondly, we design an efficient establishment quantum particle swarm optimization (EQPSO) algorithm for coalition scheduling, which is equipped with coalition similarity judgment to reduce the coalition formation time cost. The experiment results show that SQPSO guarantees a superior coalition for every task and earlier convergence in the whole task set allocation, and EQPSO gives the optimal scheduling order which reduces the total execution time.