Coral reefs are essential ecological barriers for maintaining marine ecosystem stability, biodiversity, and coastal protection. However, climate change, human activities, and harsh marine environments have accelerated coral degradation, creating an increasing demand for intelligent and low-damage restoration equipment for coral nursery planting. To address the low efficiency, high risk, and repetitive nature of diver-based operations, this paper develops an underwater robotic operation platform for coral nursery planting. By integrating visual perception, attitude stabilization, station-keeping, and close-range operation capabilities, the robot provides a stable carrier for coral seedling recognition, approach, transport, and planting, thereby improving continuous operation under complex terrain, water-flow disturbances, and limited visibility. On this basis, the dynamic coupling between the underwater robot body and manipulator operation is further considered, and a compliant control method for robot–manipulator–coral interaction is proposed. By combining end-effector trajectory planning, contact-force constraints, and coordinated compensation of the robot body attitude, the manipulator can adaptively reduce contact impact, positioning error, and operational instability during seedling grasping, posture adjustment, fixed-point placement, and fixation. Simulation analysis and underwater experimental tests are conducted to verify the effectiveness of the proposed method in end-effector trajectory tracking, contact stability, and low-damage manipulation. The results provide technical support for intelligent coral nursery planting, precise underwater robotic operation, and safe interaction control of robot–manipulator coupled systems.