Automated audio captioning is a cross-modal translation task for describing the content of audio clips with natural language sentences. This task has attracted increasing attention and substantial progress has been made in recent years. Captions generated by existing models are generally faithful to the content of audio clips, however, these machine-generated captions are often deterministic (e.g., generating a fixed caption for a given audio clip), simple (e.g., using common words and simple grammar), and generic (e.g., generating the same caption for similar audio clips). When people are asked to describe the content of an audio clip, different people tend to focus on different sound events and describe an audio clip diversely from various aspects using distinct words and grammar. We believe that an audio captioning system should have the ability to generate diverse captions, either for a fixed audio clip, or across similar audio clips. To this end, we propose an adversarial training framework based on a conditional generative adversarial network (C-GAN) to improve diversity of audio captioning systems. A caption generator and two hybrid discriminators compete and are learned jointly, where the caption generator can be any standard encoder-decoder captioning model used to generate captions, and the hybrid discriminators assess the generated captions from different criteria, such as their naturalness and semantics. We conduct experiments on the Clotho dataset. The results show that our proposed model can generate captions with better diversity as compared to state-of-the-art methods.