Computational thinking, and by extension, computer programming, is notoriously challenging to learn. Conversational agents and generative artificial intelligence (genAI) have the potential to facilitate this learning process by offering personalized guidance, interactive learning experiences, and code generation. However, current genAI-based chatbots focus on professional developers and may not adequately consider educational needs. Involving educators in conceiving educational tools is critical for ensuring usefulness and usability. We enlisted nine instructors to engage in design fiction sessions in which we elicited abilities such a conversational agent supported by genAI should display. Participants envisioned a conversational agent that guides students stepwise through exercises, tuning its method of guidance with an awareness of the educational background, skills and deficits, and learning preferences. The insights obtained in this paper can guide future implementations of tutoring conversational agents oriented toward teaching computational thinking and computer programming.