We consider numerical discretizations for nonlinear Klein-Gordon/wave equations in a rotating frame. Due to the strong centrifugal forces in the model, non-proper spatial discretizations of the rotating terms (under finite difference or finite element) would lead to numerical instability that cannot be overcome by standard time averages. We identify a class of boundary-stable type finite difference discretizations. Based on it, we propose several stable and accurate finite difference time-domain schemes with discrete conservation laws. Extensive numerical experiments and simulations are done to understand the significance of the model and the proposed schemes.