Generating stylized responses is essential to build intelligent and engaging dialogue systems. However, this task is far from well-explored due to the difficulties of rendering a particular style in coherent responses, especially when the target style is embedded only in unpaired texts that cannot be directly used to train the dialogue model. This paper proposes a stylized dialogue generation method that can capture stylistic features embedded in unpaired texts. Specifically, our method can produce dialogue responses that are both coherent to the given context and conform to the target style. In this study, an inverse dialogue model is first introduced to predict possible posts for the input responses. Then this inverse model is used to generate stylized pseudo dialogue pairs based on these stylized unpaired texts. Further, these pseudo pairs are employed to train the stylized dialogue model with a joint training process. A style routing approach is proposed to intensify stylistic features in the decoder. Automatic and manual evaluations on two datasets demonstrate that our method outperforms competitive baselines in producing coherent and style-intensive dialogue responses.