In this paper, the problem of the trajectory design for a group of energy-constrained drones operating in dynamic wireless network environments is studied. In the considered model, a team of drone base stations (DBSs) is dispatched to cooperatively serve clusters of ground users that have dynamic and unpredictable uplink access demands. In this scenario, the DBSs must cooperatively navigate in the considered area to maximize coverage of the dynamic requests of the ground users. This trajectory design problem is posed as an optimization framework whose goal is to find optimal trajectories that maximize the fraction of users served by all DBSs. To find an optimal solution for this non-convex optimization problem under unpredictable environments, a value decomposition based reinforcement learning (VDRL) solution coupled with a meta-training mechanism is proposed. This algorithm allows the DBSs to dynamically learn their trajectories while generalizing their learning to unseen environments. Analytical results show that, the proposed VD-RL algorithm is guaranteed to converge to a local optimal solution of the non-convex optimization problem. Simulation results show that, even without meta-training, the proposed VD-RL algorithm can achieve a 53.2% improvement of the service coverage and a 30.6% improvement in terms of the convergence speed, compared to baseline multi-agent algorithms. Meanwhile, the use of meta-learning improves the convergence speed of the VD-RL algorithm by up to 53.8% when the DBSs must deal with a previously unseen task.