Artificial Intelligence (AI), and particularly Large Language Models (LLMs), is reshaping healthcare by enabling more efficient, accurate, and scalable solutions for complex administrative tasks, including diagnosis coding, which remains a predominantly manual process that is time-intensive and prone to human error. Limited studies have addressed the use of AI in facilitating diagnostic coding within specialized clinical environments. To address this gap, this paper employs a qualitative participatory design science research (DSR) approach to explore the subjective experiences, needs, and expectations of healthcare professionals involved in diagnosis coding. A co-designed LLM-based prototype was developed to improve efficiency, transparency, and accountability. Data were collected through observations, interviews, and workshops, and analysed using thematic analysis, which guided the design process. Findings revealed that manual diagnosis coding is time-intensive, inconsistent, and relies on inefficient paper-based references. Participants emphasized the need for an AI-automated system that prioritizes explainability, confidence indicators, and system integration. The co-designed prototype with a dual-panel interface was validated for its simplicity, efficiency, and alignment with existing clinical routines. This study advances the understanding of human-AI collaboration in healthcare administration while providing practical guidance for implementing integrated, explainable systems that transform manual coding to quality validation in AI-assisted diagnosis coding workflows.