Stance detection is the computational task of determining the attitude (e.g., for, against, neutral) expressed in text toward a specific target topic. In its more conventional form, the task focuses on isolated, context-free input utterances. Conversational stance detection, by contrast, analyzes messages embedded within dialogue threads, enabling the interpretation of responses in relation to preceding discourse, and takes into account a greater variety of stance relations (e.g., support, deny, query, comment, etc.). Despite growing research attention, however, conversational stance detection remains relatively under-resourced and largely limited to the English language. To address these gaps, this study introduces CoSt-BR, a new corpus for conversational stance detection composed of a large set of annotated Reddit discussions in Brazilian Portuguese. In addition, the paper also reports benchmark results obtained using various computational methods, including supervised and prompt-based strategies, applied to the corpus data, providing baseline references for future research in this area.