The stochastic variational method (SVM) is one of the most powerful methods to solve quantum few-body systems precisely in various fields, such as nuclear and atomic physics. To the best of our knowledge, no SVM code optimized for GPUs has been reported. We developed a parallel SVM code for few-body clusters of $^4$He atoms and optimized it for two GPU architectures, NVIDIA GH200 and AMD Instinct MI300A, with the entire code written by an AI coding agent. On the algorithmic side, we introduce the secular-equation method with the Gu--Eisenstat prescription for solving the generalized eigenvalue problem within the SVM framework. The main part of the code tuning is to batch the many small matrices so that the GPUs are used efficiently, together with an array layout in memory optimized for coalesced addressing. For the five-body system with 4800 SVM basis states, the tuned SVM code runs 16.2 (14.7) times faster on the NVIDIA GH200 (AMD MI300A) than the same tuned code on the Intel Xeon Max CPU system, and 168 (153) times faster than the first working CPU implementation. The achieved performance brings 6-body and larger cluster systems within reach.

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