Emotion coping is inherently relational, unfolding through interactions with friends, family, professionals, and communities. Yet AI chatbots are largely designed around a user--AI dyad. Learning from the ethics of care, we examine how AI chatbots shape the relational conditions of emotion coping. We conducted a scenario-based study with 17 U.S. young adults across four emotion coping scenarios. Participants identified eight roles through which AI could support relational conditions, alongside three challenges: flattening distinct relational conditions, discouraging reciprocity, and shifting relational labor onto users. This study contributed a relational perspective of responsible AI in emotion coping. We argue that responsible AI should respond to individuals' situated relational conditions rather than provide general-purpose support. We further identify two design principles: fostering reciprocity by supplying materials to engage with others, and strengthening emotional self-efficacy. Together, we position responsible AI as AI in the loop of human relationships.

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