The lack of large and diverse discourse treebanks hinders the application of data-driven approaches, such as deep-learning, to RSTstyle discourse parsing. In this work, we present a novel scalable methodology to automatically generate discourse treebanks using distant supervision from sentiment-annotated datasets, creating and publishing MEGA-DT, a new large-scale discourse-annotated corpus. Our approach generates discourse trees incorporating structure and nuclearity for documents of arbitrary length by relying on an efficient heuristic beam-search strategy, extended with a stochastic component. Experiments on multiple datasets indicate that a discourse parser trained on our MEGA-DT treebank delivers promising inter-domain performance gains when compared to parsers trained on human-annotated discourse corpora.