In many low-to-middle income (LMIC) countries, ultrasound is used for assessment of pleural effusion. Typically, the extent of the effusion is manually measured by a sonographer, leading to significant intra-/inter-observer variability. In this work, we investigate the use of deep learning (DL) to automate the process of pleural effusion segmentation from ultrasound images. On two datasets acquired in a LMIC setting, we achieve median Dice Similarity Coefficients (DSCs) of 0.82 and 0.74 respectively using the nnU-net DL model. We also investigate the use of coordinate convolutions in the DL model and find that this results in a statistically significant improvement in the median DSC on the first dataset to 0.85, with no significant change on the second dataset. This work showcases, for the first time, the potential of DL in automating the process of effusion assessment from ultrasound in LMIC settings where there is often a lack of experienced radiologists to perform such tasks.