Conformal array is attractive due to its flexibility to attach to different shape of surface. However, beam pattern synthesis for conformal array to control power side lobes and different polarization components for two dimensional angle space is a challenge, especially the degree of freedom is limited. In this work, we propose a robust beam pattern synthesis formulation for conformal array based on constrained convex optimization. By penalizing the maximum gain of cross-polarization component levels, power side lobes and different polarization components are controlled in a manner that the number of constraints is no longer limited by the array DoF. The proposed formulation is a convex second-order cone programming, a computationally efficient algorithm based on the alternating directions of multipliers method is designed to solve it. Simulations demonstrate the effectiveness of the proposed formulation to synthesize a desired pattern with robustness.