Multi-document question generation focuses on generating a question that covers the common aspect of multiple documents. However, models trained only using the targeted ("positive") document set generate questions that are generic i.e. they cover a larger scope than delineated by the document set. To address this challenge, we introduce the contrastive learning strategy where given "positive" and "negative" sets of documents, we generate a question that is closely related to the "positive" set but is far away from the "negative" set. This setting allows generated questions to be more specific and related to the target document set. To generate such specific questions, we propose Multi-Source Coordinated Question Generator (MSCQG), a novel framework that includes a supervised learning (SL) stage and a reinforcement learning (RL) stage. In the SL stage, a single-document question generator is trained. In the RL stage, a coordinator model is trained to find optimal attention weights among multiple single-document generator instances, by optimizing a reward designed to promote specificity of generated questions. We also develop an effective auxiliary objective, named Set-induced Contrastive Regularization (SCR) that improves the coordinator's contrastive learning during the RL stage. We show that our model significantly outperforms several strong baselines based on retrieval and neural generation, as measured by automatic metrics and human evaluation.