The ability to solve motion-planning queries within a fixed time budget is critical for deploying robotic systems in time-sensitive applications. Semi-static environments, where most of the workspace remains fixed while a subset of obstacles varies between tasks, exhibit structured variability that can be exploited to provide stronger guarantees than general-purpose planners. However, existing approaches either lack formal coverage guarantees or rely on discretizations of obstacle configurations that restrict applicability to realistic domains. This paper introduces COVER, a framework that incrementally constructs coverage-verified roadmaps for semi-static environments. COVER decomposes the arrangement space by independently partitioning the configuration space of each movable obstacle and verifies roadmap feasibility within each partition, enabling fixed-time query resolution for verified regions.We evaluate COVER on a 7-DoF manipulator performing object-picking in tabletop and shelf environments, demonstrating broader problem-space coverage and higher query success rates than prior work, particularly with obstacles of different sizes.