This paper addresses user-specific dialogs. In contrast to previous research on personalized dialogue focused on achieving virtual user dialogue as defined by persona descriptions, user-specific dialogue aims to reproduce real-user dialogue beyond persona-based dialogue. Fine-tuning using the target user's dialogue history is an efficient learning method for a user-specific model. However, it is prone to overfitting and model destruction due to the small amount of data. Therefore, we propose a learning method for user-specific models by combining parameter-efficient fine-tuning with a pre-trained dialogue model that includes user profiles. Parameter-efficient fine-tuning adds a small number of parameters to the entire model, so even small amounts of training data can be trained efficiently and are robust to model destruction. In addition, the pre-trained model, which is learned by adding simple prompts for automatically inferred user profiles, can generate speech with enhanced knowledge of the user's profile, even when there is little training data during fine-tuning. In experiments, we compared the proposed model with large-language-model utterance generation using prompts containing users' personal information. Experiments reproducing real users' utterances revealed that the proposed model can generate utterances with higher reproducibility than the compared methods, even with a small model.