Several variations of the Watterson estimator of variability for Next Generation Sequencing (NGS) data have been proposed in the literature. We present a unified framework for generalized Watterson estimators based on Maximum Composite Likelihood, which encompasses most of the existing estimators. We propose this class of unbiased estimators as generalized Watterson estimators for a large class of NGS data, including pools and trios. We also discuss the relation with the estimators proposed in the literature and show that they admit two equivalent but seemingly different forms, deriving a set of combinatorial identities as a byproduct. Finally, we give a detailed treatment of Watterson estimators for single or multiple autopolyploid individuals.