This paper presents a Center of Mass (CoM) based manipulation and regrasp planner that implements stability constraints to preserve the robot balance. The planner provides a graph of IK-feasible, collision-free and stable motion sequences, constructed using an energy based motion planning algorithm. It assures that the assembly motions are stable and prevent the robot from falling while performing dexterous tasks in different situations. Furthermore, the constraints are also used to perform an RRT-inspired task-related stability estimation in several simulations. The estimation can be used to select between single-arm and dual-arm regrasping configurations to achieve more stability and robustness for a given manipulation task. To validate the planner and the task-related stability estimations, several tests are performed in simulations and real-world experiments involving the HRP5P humanoid robot, the 5th generation of the HRP robot family. The experiment results suggest that the planner and the task-related stability estimation provide robust behavior for the humanoid robot while performing regrasp tasks.