Plastic pollution is a critical global issue. Increases in plastic consumption have triggered increased production, which in turn has led to increased plastic disposal. In situ observation of plastic litter is tedious and cumbersome, especially in rural areas and around transboundary rivers. We therefore propose automatic mapping of plastic in rivers using unmanned aerial vehicles (UAVs) and deep learning (DL) models that require modest compute resources. We evaluate the method at two different sites: the Houay Mak Hiao River, a tributary of the Mekong River in Vientiane, Laos, and Khlong Nueng canal in Talad Thai, Khlong Luang, Pathum Thani, Thailand. Detection models in the You Only Look Once (YOLO) family are evaluated in terms of runtime resources and mean average Precision (mAP) at an Intersection over Union (IoU) threshold of 0.5. YOLOv5s is found to be the most effective model, with low computational cost and a very high mAP of 0.81 without transfer learning for the Houay Mak Hiao dataset. The performance of all models is improved by transfer learning from Talad Thai to Houay Mak Hiao. Pre-trained YOLOv4 with transfer learning obtains the overall highest accuracy, with a 3.0% increase in mAP to 0.83, compared to the marginal increase of 2% in mAP for pre-trained YOLOv5s. YOLOv3, when trained from scratch, shows the greatest benefit from transfer learning, with an increase in mAP from 0.59 to 0.81 after transfer learning from Talad Thai to Houay Mak Hiao. The pre-trained YOLOv5s model using the Houay Mak Hiao dataset is found to provide the best tradeoff between accuracy and computational complexity, requiring model resources yet providing reliable plastic detection with or without transfer learning. Various stakeholders in the effort to monitor and reduce plastic waste in our waterways can utilize the resulting deep learning approach irrespective of location.