Composite materials are vital in aerospace for their exceptional strength-to-weight ratio. This study delves into reliability-based optimisation of composite plates within aeroelastic constraints, employing an efficient global optimisation method and genetic algorithms. Initial analysis focuses on aeroelastic responses such as limit flutter speed, gust response, and static loads, emphasizing maximum strain assessment. To tackle optimisation challenges of composite stacking sequences, a homogenization technique with lamination parameters is applied. We then formulate a constrained optimisation problem to minimize gust response while meeting flutter and maximum strain constraints. Surrogate models based on conditioned Gaussian Processes are developed for each aeroelastic response, facilitating optimisation within the composite design space. These models, with potential for local refinement, expedite optimal solution identification. Further, we integrate reliability-based optimisation into the framework to determine a robust stacking sequence using genetic algorithms, accounting for random fiber orientation variations. This holistic approach integrates aeroelastic analysis, constrained optimisation, surrogate modeling, and reliability-based optimisation, proving effective in designing reliable, efficient composite structures for aerospace, thus enhancing performance and safety.