Sleep staging is critical for assessing sleep quality and tracking health. Polysomnography (PSG) provides comprehensive multimodal sleep-related information, but its complexity and impracticality limit its practical use in daily and ubiquitous monitoring. Conversely, unimodal devices offer more convenience but less accuracy. Existing multimodal learning paradigms typically assume that the data types remain consistent between the training and testing phases. This makes it challenging to leverage information from other modalities in ubiquitous scenarios (e.g., at home) where only one modality is available. To address this issue, we introduce a novel framework for ubiquitous Sleep staging via Supervised Multimodal Coordination, called SleepSMC. To capture category-related consistency and complementarity across modality-level instances, we propose supervised modality-level instance contrastive coordination. Specifically, modality-level instances within the same category are considered positive pairs, while those from different categories are considered negative pairs. To explore the varying reliability of auxiliary modalities, we calculate uncertainty estimates based on the variance in confidence scores for correct predictions during multiple rounds of random masks. These uncertainty estimates are employed to assign adaptive weights to multiple auxiliary modalities during contrastive learning, ensuring that the primary modality learns from high-quality, category-related features. Experimental results on four public datasets, ISRUC-S3, MASS-SS3, Sleep-EDF-78, and ISRUC-S1, show that SleepSMC achieves state-of-the-art cross-subject performance. SleepSMC significantly improves performance when only one modality is present during testing, making it suitable for ubiquitous sleep monitoring.