Singing Voice Synthesis (SVS) aims to generate expressive vocal performances from structured musical inputs such as lyrics and pitch sequences. While recent progress in discrete codec-based speech synthesis has enabled zero-shot generation via in-context learning, directly extending these techniques to SVS remains non-trivial due to the requirement for precise melody control. In particular, prompt-based generation often introduces prosody leakage, where pitch information is inadvertently entangled within the timbre prompt, compromising controllability. We present CoMelSinger, a zero-shot SVS framework that enables structured and disentangled melody control within a discrete codec modeling paradigm. Built on the non-autoregressive MaskGCT architecture, CoMelSinger replaces conventional text inputs with lyric and pitch tokens, preserving in-context generalization while enhancing melody conditioning. To suppress prosody leakage, we propose a coarse-to-fine contrastive learning strategy that explicitly regularizes pitch redundancy between the acoustic prompt and melody input. Furthermore, we incorporate a lightweight encoder-only Singing Voice Transcription (SVT) module to align acoustic tokens with pitch and duration, offering fine-grained frame-level supervision. Experimental results demonstrate that CoMelSinger achieves notable improvements in pitch accuracy, timbre consistency, and zero-shot transferability over competitive baselines. Audio samples are available at https://danny-nus.github.io/CoMelSinger/.