Deep learning (DL) based resource allocation (RA) has recently gained significant attention due to its performance efficiency. However, most related studies assume an ideal case where the number of users and their utility demands, e.g., data rate constraints, are fixed, and the designed DL-based RA scheme exploits a policy trained only for these fixed parameters. Consequently, computationally complex policy retraining is required whenever these parameters change. In this paper, we introduce a DL-based resource allocator (ALCOR) that allows users to adjust their utility demands freely, such as based on their application layer requirements. ALCOR employs deep neural networks (DNNs) as the policy in a time-sharing problem. The underlying optimization algorithm iteratively optimizes the on-off status of users to satisfy their utility demands in expectation. The policy performs unconstrained RA (URA) -- RA without considering user utility demands -- among active users to maximize the sum utility (SU) at each time instant. Depending on the chosen URA scheme, ALCOR can perform RA in either a centralized or distributed scenario. The derived convergence analyses provide theoretical guarantees for ALCOR's convergence, and numerical experiments corroborate its effectiveness compared to meta-learning and reinforcement learning approaches.