Despite recent progress in language models, generating constrained text for specific domains remains a challenge, particularly when utilizing black-box models that lack domain-specific knowledge. In this paper, we introduce ScoPE (Score-based Progressive Editor) generation, a novel approach for controlled text generation for black-box language models. We employ ScoPE to facilitate text generation in the target domain by integrating it with language models through a cascading approach. Trained to enhance the target domain score of the edited text, ScoPE progressively edits intermediate output discrete tokens to align with the target attributes throughout the auto-regressive generation process of the language model. This iterative process guides subsequent steps to produce desired output texts for the target domain. Our experimental results on diverse controlled generations demonstrate that ScoPE effectively facilitates controlled text generation for black-box language models in both in-domain and out-of-domain conditions, which is challenging for existing methods.