An innovative conformal array synthesis approach is proposed which exploits a generalization of the Bayesian Compressive Sampling (BCS) technique. Towards this end, the design problem is mathematically formulated in terms of a Bayesian learning one with sparseness priors. The arising functional is then solved by means of a suitable Relevance Vector Machine (RVM) technique. Numerical results are reported to assess the effectiveness of the proposed approach in the synthesis of conformal sparse arrays.