This paper investigates the covert communications via spectrum allocations in a cellular-enabled unmanned aerial vehicle (UAV) network consisting of a base station (BS), UAVs, ground users (GUs), and a warden, where warden attempts to detect the transmission from a target GU to a UAV receiver. We formulate the spectrum allocation as an optimization problem with the constraints of covertness performance requirement and the qualities of service (QoS) of cellular communications. This is a nonlinear and nonconvex problem, which is generally challenging to be solved. Thus, we propose a deep reinforcement learning (DRL) approach to solve it. Under such an approach, we first model the multi-agent DRL environment in such networks. Then we define the state, action, reward and interaction mechanism of the DRL environment. Finally, a DRL algorithm is presented for learning the optimal policy of spectrum allocation.