A wide variety of resource allocation problems operate under resource constraints that are managed by a central arbitrator, with agents who evaluate and communicate preferences over these resources. We formulate this broad class of problems as Distributed Evaluation, Centralized Allocation (DECA) problems and propose methods to learn fair and efficient policies in centralized resource allocation. Our methods are applied to learning long-term fairness in a novel and general framework for fairness in multi-agent systems. We show three different methods based on Double Deep Q-Learning: (1) A joint weighted optimization of fairness and utility, (2) a split optimization, learning two separate Q-estimators for utility and fairness, and (3) an online policy perturbation to guide existing black-box utility functions toward fair solutions. Our methods outperform existing fair MARL approaches on multiple resource allocation domains, even when evaluated using diverse fairness functions, and allow for flexible online trade-offs between utility and fairness.