TalkPlayData 2 is a synthetic dataset for multimodal conversational music recommendation generated through an agent-based data pipeline. This pipeline generates multiple large-scale language model (LLM) agents with various roles and specialized prompts, and records conversations between the Listener LLM and the Recsys LLM to obtain chat data. To address diverse conversational scenarios, the Listener LLM in each conversation is conditioned on fine-tuned conversational objectives. All LLMs are multimodal, including audio and images, enabling multimodal recommendation and conversation simulation. In LLM-as-a-judge and subjective evaluation experiments, TalkPlayData 2 achieved its goals across various aspects relevant to training a music generation recommendation model.