As an indispensable ingredient of intelligence, commonsense reasoning is crucial for large language models (LLMs) in real-world scenarios. In this paper, we propose CORECODE, a dataset that contains abundant commonsense knowledge manually annotated on dyadic dialogues, to evaluate the commonsense reasoning and commonsense conflict detection capabilities of Chinese LLMs. We categorize commonsense knowledge in everyday conversations into three dimensions: entity, event, and social interaction. For easy and consistent annotation, we standardize the form of commonsense knowledge annotation in open-domain dialogues as "domain: slot = value". A total of 9 domains and 37 slots are defined to capture diverse commonsense knowledge. With these pre-defined domains and slots, we collect 76,787 commonsense knowledge annotations from 19,700 dialogues through crowdsourcing. To evaluate and enhance the commonsense reasoning capability for LLMs on the curated dataset, we establish a series of dialogue-level reasoning and detection tasks, including commonsense knowledge filling, commonsense knowledge generation, commonsense conflict phrase detection, domain identification, slot identification, and event causal inference. A wide variety of existing open-source Chinese LLMs are evaluated with these tasks on our dataset. Experimental results demonstrate that these models are not competent to predict CORECODE's plentiful reasoning content, and even ChatGPT could only achieve 0.275 and 0.084 accuracy on the domain identification and slot identification tasks under the zero-shot setting. We release the data and codes of CORECODE at https://github.com/danshi777/CORECODE to promote commonsense reasoning evaluation and study of LLMs in the context of daily conversations.