We consider the downlink of cellular systems in which the users have Quality of Service (QoS) requirements, and we study the design of robust fair broadcasting schemes that maximize the minimum QoS over all users when the users' channel state information (CSI) is imperfect at the transmitter. Using a bounded uncertainty model for the transmitter's estimate of users' channels we formulate each user's QoS requirement as a constraint on the mean square error (MSE) in its received signal, and we demonstrate that these MSE constraints imply constraints on the received signal- to-interference-plus-noise-ratio (SINR) of each user. Using these MSE constraints, we present a unified design approach for robust linear and non-linear transceivers with QoS requirements, and we provide quasi-convex formulations that can be efficiently solved using a one-dimensional bisection search. The proposed designs overcome the limitations of existing approaches that only provide conservative solutions and only applicable to the case of linear preceding. Furthermore, we provide tractable and computationally-efficient design formulations for a quite general model of channel uncertainty that subsumes many uncertainty regions. Our numerical results demonstrate that in the presence of uncertainty in the transmitter's knowledge of users' channels, the proposed designs provide guarantees to a larger set of minimum QoS requirements than existing approaches.