Man, most of the tension I see writers build between Kanao and Nezuko stems from that fundamental difference in their origins. Kanao was raised to be this emotionless tool, her feelings drilled out of her, while Nezuko's entire demon nature is governed by a powerful, protective emotional core, even if she can't speak. It's not about them fighting each other, but about Kanao trying to understand something so alien to her—raw, instinctive compassion. That internal conflict for Kanao is gold to write about.
I've read a few stories that really dig into the aftermath of the final battle, where Kanao, now trying to live a normal life with her emotions returning, is utterly bewildered by Nezuko's simplicity and warmth. Nezuko doesn't hold grudges, doesn't overthink. Kanao would analyze every interaction, every gesture, trying to calculate the proper emotional response, and Nezuko would just hand her a flower. The drama comes from that frustrating, beautiful gap in their communication styles.
Sometimes the external conflict is just the world not understanding. The Corps is disbanded, but old prejudices linger. A story I liked had them running a small clinic together, and former slayers or wary villagers would question their partnership. The conflict wasn't violent, just this constant, low-grade societal pressure that forced them to rely on each other even more, which in turn forced Kanao to confront her own past more directly than if she were alone.