The customization of large language models (LLMs) for user-specified tasks gets important. However, maintaining all the customized LLMs on cloud servers incurs substantial memory and computational overheads, and uploading user data can also lead to privacy concerns. On-device LLMs can offer a promising solution by mitigating these issues. Yet, the performance of on-device LLMs is inherently constrained by the limitations of small-scaled models. To overcome these restrictions, we first propose Crayon, a novel approach for on-device LLM customization. Crayon begins by constructing a pool of diverse base adapters, and then we instantly blend them into a customized adapter without extra training. In addition, we develop a device-server hybrid inference strategy, which deftly allocates more demanding queries or non-customized tasks to a larger, more capable LLM on a server. This ensures optimal performance without sacrificing the benefits of on-device customization. We carefully craft a novel benchmark from multiple question-answer datasets, and show the efficacy of our method in the LLM customization.