Graph Neural Networks (GNNs) present a fundamental hardware challenge by fusing irregular, memory-bound graph traversals with regular, compute-intensive dense matrix operations. While frameworks such as PyTorch Geometric (PyG) and Deep Graph Library (DGL) prioritize high-level usability, they fail to address these divergent execution characteristics. As a result, they rely on generic kernels that suffer from poor cache locality, excessive memory movement, and substantial intermediate allocations. To address these limitations, we present Morphling, a domain-specific code synthesizer designed to bridge this gap. Morphling compiles high-level GNN specifications into portable, backend-specialized implementations targeting OpenMP, CUDA, and MPI. It achieves this by instantiating a library of optimized, architecture-aware primitives tailored to each execution environment. Morphling also incorporates a runtime sparsity-aware execution engine that dynamically selects dense or sparse execution paths using input feature statistics, reducing unnecessary computation on zero-valued entries. We evaluate Morphling on eleven real-world datasets spanning diverse graph structures, feature dimensionalities, and sparsity regimes. Morphling improves per-epoch training throughput by an average of 20X on CPUs, 19X on GPUs, and 6X in distributed settings over PyG and DGL, with peak speedups reaching 66X. Morphling's memory-efficient layouts further reduce peak memory consumption by up to 15X, enabling large-scale GNN training on commodity hardware. These findings demonstrate that specialized, architecture-aware code synthesis provides an effective and scalable path toward high-performance GNN execution across diverse parallel and distributed platforms.