Examples in web API specifications can be essential for API testing, API understanding, and even building chat-bots for APIs. Unfortunately, most API specifications lack human written examples. This paper introduces a novel technique for generating examples for web API specifications. We start from in-context learning (ICL): given an API parameter, use a prompt context containing a few examples from other similar API parameters to call a model to generate new examples. However, while ICL tends to generate correct examples, those lack diversity, which is also important for most downstream tasks. Therefore, we extend the technique to iterated-calls ICL (ICICL): use a few different prompt contexts, each containing a few examples, to iteratively call the model with each context. Our intrinsic evaluation demonstrates that ICICL improves both correctness and diversity of generated examples. More importantly, our extrinsic evaluation demonstrates that those generated examples significantly improve the performance of downstream tasks of testing, understanding, and chat-bots for APIs.