We propose a real-time implementable motion planning technique for cooperative object transportation by nonholonomic mobile manipulator robots (MMRs) in an environment with static and dynamic obstacles. The proposed motion planning technique works in two steps. A novel visibility vertices-based path planning algorithm computes a global piece-wise linear path between the start and the goal location in the presence of static obstacles offline. It defines the static obstacle free space around the path with a set of convex polygons for the online motion planner. We employ a Nonliner Model Predictive Control (NMPC) based online motion planning technique for nonholonomic MMRs that jointly plans for the mobile base and the manipulators arm. It efficiently utilizes the locomotion capability of the mobile base and the manipulation capability of the arm. The motion planner plans feasible motion for the MMRs and generates trajectory for object transportation considering the kinodynamic constraints and the static and dynamic obstacles. The efficiency of our approach is validated by numerical simulation and hardware experiments in varied environments.