Depression is a major contributor to the mental-health burden in Nigeria, yet screening coverage remains limited due to low access to clinicians, stigma, and language barriers. Traditional tools like the Patient Health Questionnaire-9 (PHQ-9) were validated in high-income countries but may be linguistically or culturally inaccessible for low- and middle-income countries and communities such as Nigeria where people communicate in Nigerian Pidgin and more than 520 local languages. This study presents a novel approach to automated depression screening using fine-tuned large language models (LLMs) adapted for conversational Nigerian Pidgin. We collected a dataset of 432 Pidgin-language audio responses from Nigerian young adults aged 18-40 to prompts assessing psychological experiences aligned with PHQ-9 items, performed transcription, rigorous preprocessing and annotation, including semantic labeling, slang and idiom interpretation, and PHQ-9 severity scoring. Three LLMs - Phi-3-mini-4k-instruct, Gemma-3-4B-it, and GPT-4.1 - were fine-tuned on this annotated dataset, and their performance was evaluated quantitatively (accuracy, precision and semantic alignment) and qualitatively (clarity, relevance, and cultural appropriateness). GPT-4.1 achieved the highest quantitative performance, with 94.5% accuracy in PHQ-9 severity scoring prediction, outperforming Gemma-3-4B-it and Phi-3-mini-4k-instruct. Qualitatively, GPT-4.1 also produced the most culturally appropriate, clear, and contextually relevant responses. AI-mediated depression screening for underserved Nigerian communities. This work provides a foundation for deploying conversational mental-health tools in linguistically diverse, resource-constrained environments.