Pre-training large language models (LLMs) on vast text corpora enhances natural language processing capabilities but risks encoding social biases, particularly gender bias. While parameter-modification methods like fine-tuning mitigate bias, they are resource-intensive, unsuitable for closed-source models, and lack adaptability to evolving societal norms. Instruction-based approaches offer flexibility but often compromise task performance. To address these limitations, we propose $\textit{FaIRMaker}$, an automated and model-independent framework that employs an $\textbf{auto-search and refinement}$ paradigm to adaptively generate Fairwords, which act as instructions integrated into input queries to reduce gender bias and enhance response quality. Extensive experiments demonstrate that $\textit{FaIRMaker}$ automatically searches for and dynamically refines Fairwords, effectively mitigating gender bias while preserving task integrity and ensuring compatibility with both API-based and open-source LLMs.