Image emotion classification (IEC) aims to extract the abstract emotions evoked in images. Recently, language-supervised methods such as contrastive language-image pretraining (CLIP) have demonstrated superior performance in image understanding. However, the underexplored task of IEC presents three major challenges: a tremendous training objective gap between pretraining and IEC, shared suboptimal prompts, and invariant prompts for all instances. In this study, we propose a general framework that effectively exploits the language-supervised CLIP method for the IEC task. First, a prompt-tuning method that mimics the pretraining objective of CLIP is introduced, to exploit the rich image and text semantics associated with CLIP. Subsequently, instance-specific prompts are automatically composed, conditioning them on the categories and image content of instances, diversifying the prompts, and thus avoiding suboptimal problems. Evaluations on six widely used affective datasets show that the proposed method significantly outperforms state-of-the-art methods (up to 9.29% accuracy gain on the EmotionROI dataset) on IEC tasks with only a few trained parameters. The code is publicly available at https://github.com/dsn0w/PT-DPC/ for research purposes.