In this paper, we address the challenging problem of path-following control for a group of $n$ Quadrotor-Slung-Load Systems (QSLSs) subject to time-varying disturbances. A single QSLS consists of a quadrotor vehicle and a load attached to the vehicle's center of mass via a cable. We propose a distributed path coordination framework that generates $n$ desired paths for the $n$ loads while maintaining a fixed inter-load formation pattern. Furthermore, we introduce a robust controller for each of the $n$ quadrotors to drive the respective load along the assigned path. The path-following controller is designed to ensure that the quadrotor thrust remains bounded with respect to position and velocity tracking errors. We present a series of simulation and experimental results to validate the effectiveness of the proposed approach and demonstrate its performance.