While autoencoders have been used as an unsupervised machine learning technique for classification and dimensionality reduction of the input data, they are lossy in nature when used alone in data compression. In this work, we proposed an image coding scheme by using stacked autoencoders, where the reconstruction residuals were entropy-coded to achieve lossless compression. As a case study, we compressed labeled red blood cell images from a database curated by pathologists for malaria infection diagnosis. Specifically, we trained two separate stacked autoencoders to automatically learn the discriminative features from input images of infected and non-infected cells. Subsequently, the residuals of these two classes of images were coded by two independent Golomb-Rice encoders. Testing results showed that this deep learning approach provided remarkably higher compression on average than several other lossless coding methods including JPEG-LS, JPEG 2000 lossless mode, and CALIC.