Domain shift poses a significant challenge in cross-domain spoken language recognition (SLR) by reducing its effectiveness. Unsupervised domain adaptation (UDA) algorithms have been explored to address domain shifts in SLR without relying on class labels in the target domain. One successful UDA approach focuses on learning domain-invariant representations to align feature distributions between domains. However, disregarding the class structure during the learning process of domain-invariant representations can result in over-alignment, negatively impacting the classification task. To overcome this limitation, we propose an optimal transport (OT)-based UDA algorithm for a cross-domain SLR, leveraging the distribution geometry structure-aware property of OT. An OT-based discrepancy measure on a joint distribution over feature and label information is considered during domain alignment in OT-based UDA. Our previous study discovered that completely aligning the distributions between the source and target domains can introduce a negative transfer, where classes or irrelevant classes from the source domain map to a different class in the target domain during distribution alignment. This negative transfer degrades the performance of the adaptive model. To mitigate this issue, we introduce coupling-weighted partial optimal transport (POT) within our UDA framework for SLR, where soft weighting on the OT coupling based on transport cost is adaptively set during domain alignment. A cross-domain SLR task was used in the experiments to evaluate the proposed UDA. The results demonstrated that our proposed UDA algorithm significantly improved the performance over existing UDA algorithms in a cross-channel SLR task.