Large language models (LLMs) like GitHub Copilot and ChatGPT have emerged as powerful tools for code generation, significantly enhancing productivity and accelerating software development. However, existing benchmarks primarily focus on general code generation without considering API-oriented code generation, i.e., generating code that invokes APIs from specific libraries. Given the growing demand for API-oriented code generation, there is a pressing need for a systematic and automated approach to evaluate LLM on API-oriented code generation. To address this gap, we propose AutoAPIEval, a lightweight and automated framework designed to evaluate the capabilities of LLMs in API-oriented code generation. Our framework works with any library that provides API documentation and focuses on two unit tasks: API recommendation and code example generation, along with four metrics to evaluate the generated APIs and code examples, such as the proportion of incorrect API recommendations for Task 1, and the proportion of code examples where no specific API is invoked and uncompilable/unexecutable code examples for Task 2. In addition, we conducted a case study on three LLMs (ChatGPT, MagiCoder, and DeepSeek Coder) and Java Runtime Environment 8 to demonstrate the framework's effectiveness. Our findings reveal substantial variability in LLM performance across tasks, with ChatGPT adhering better to instructions, while sharing similar effectiveness in code example generation with its counterparts (i.e., MagiCoder and DeekSeek Coder). We also identify key factors associated with code quality, such as API popularity and model confidence, and build classifiers that achieve high accuracy in detecting incorrect API recommendations and erroneous code examples. Retrieval-augmented generation enhances the quality of code generated by LLMs, though its effectiveness varies across different LLMs.