Recent advances in Large Language Models (LLMs) have shown promise in automating discourse annotation for conversations. While manually designing tree annotation schemes significantly improves annotation quality for humans and models, their creation remains time-consuming and requires expert knowledge. We propose a fully automated pipeline that uses LLMs to construct such schemes and perform annotation. We evaluate our approach on speech functions (SFs) and the Switchboard-DAMSL (SWBD-DAMSL) taxonomies. Our experiments compare various design choices, and we show that frequency-guided decision trees, paired with an advanced LLM for annotation, can outperform previously manually designed trees and even match or surpass human annotators while significantly reducing the time required for annotation. We release all code and resultant schemes and annotations to facilitate future research on discourse annotation.