Unsupervised domain adaptation (UDA) is a challenging open problem in land cover mapping. Previous studies show encouraging progress in addressing cross-domain distribution shifts on remote sensing benchmarks for land cover mapping. The existing works are mainly built on large neural network architectures, which makes them resource-hungry systems, limiting their practical impact for many real-world applications in resource-constrained environments. Thus, we proposed a simple yet effective framework to search for lightweight neural networks automatically for land cover mapping tasks under domain shifts. This is achieved by integrating Markov random field neural architecture search (MRF-NAS) into a self-training UDA framework to search for efficient and effective networks under a limited computation budget. This is the first attempt to combine NAS with self-training UDA as a single framework for land cover mapping. We also investigate two different pseudo-labelling approaches (confidence-based and energy-based) in self-training scheme. Experimental results on two recent datasets (OpenEarthMap & FLAIR #1) for remote sensing UDA demonstrate a satisfactory performance. With only less than 2M parameters and 30.16 GFLOPs, the best-discovered lightweight network reaches state-of-the-art performance on the regional target domain of OpenEarthMap (59.38% mIoU) and the considered target domain of FLAIR #1 (51.19% mIoU). The code is at https://github.com/cliffbb/UDA-NAS}{https://github.com/cliffbb/UDA-NAS.