Multi-stakeholder recommender systems (RSs) are a major paradigm shift from current RSs because recommendations affect not only item consumers (end-users) but also item providers (owners). They also motivate the need for new performance metrics beyond recommendation quality that explicitly affect the latter. In this work, we introduce a framework for optimizing multi-stakeholder RSs under constraints on diversity and coverage. Our goal is to make recommendations to end-users while treating each item provider equally, by ensuring sufficient user base coverage and diverse profiles of users to which items are recommended. Namely, items of each provider should be recommended to a certain number of users that are also diverse enough in their preferences. The optimization objective is that the total average rating of recommended items is as close as possible to that of a baseline RS. The problem is formulated as a quadratically constrained integer program, which is NP-Hard and impractical to solve in the presence of big data and many providers. Interestingly, we show that when only the coverage constraint exists, an instance of the problem can be solved optimally in polynomial time through its Linear Programming relaxation, and this solution can be used to initialize a low-complexity heuristic algorithm. Data experiments show good performance and demonstrate the impact of these constraints on average rating of recommended items.