South Africa's escalating mental health crisis, compounded by limited access to culturally responsive care, calls for innovative and contextually grounded interventions. While large language models show considerable promise for mental health support, their predominantly Western-centric training data limit cultural and linguistic applicability in African contexts. This study introduces a proof-of-concept framework that integrates cognitive behavioral therapy with the African philosophy of Ubuntu to create a culturally sensitive, emotionally intelligent, AI-driven mental health dialogue system. Guided by a design science research methodology, the framework applies both deep theoretical and therapeutic adaptations as well as surface-level linguistic and communicative cultural adaptations. Key CBT techniques, including behavioral activation and cognitive restructuring, were reinterpreted through Ubuntu principles that emphasize communal well-being, spiritual grounding, and interconnectedness. A culturally adapted dataset was developed through iterative processes of language simplification, spiritual contextualization, and Ubuntu-based reframing. The fine-tuned model was evaluated through expert-informed case studies, employing UniEval for conversational quality assessment alongside additional measures of CBT reliability and cultural linguistic alignment. Results demonstrate that the model effectively engages in empathetic, context-aware dialogue aligned with both therapeutic and cultural objectives. Although real-time end-user testing has not yet been conducted, the model underwent rigorous review and supervision by domain specialist clinical psychologists. The findings highlight the potential of culturally embedded emotional intelligence to enhance the contextual relevance, inclusivity, and effectiveness of AI-driven mental health interventions across African settings.