Purpose: To develop a fully automatic method, based on deep learning algorithms, for determining the locations of cone photoreceptors within adaptive optics scanning laser ophthalmoscope images and evaluate its performance against a dataset of manually segmented images. Methods: A fully convolutional network (FCN) based on U-Net architecture was used to generate prediction probability maps and then used a localization algorithm to reduce the prediction map to a collection of points. The proposed method was trained and tested on two publicly available datasets of different imaging modalities, with Dice overlap, false discovery rate, and true positive reported to assess performance. Results: The proposed method achieves a Dice coefficient of 0.989, true positive rate of 0.987, and false discovery rate of 0.009 on the first confocal dataset; and a Dice coefficient of 0.926, true positive rate of 0.909, and false discovery rate of 0.051 on the second split detector dataset. Results compare favorably with a previously proposed method, but this method provides quicker (25 times faster) evaluation performance. Conclusions: The proposed FCN-based method demonstrates that deep learning algorithms can achieve accurate cone localizations, almost comparable to a human expert, while labeling the images. Translational Relevance: Manual cone photoreceptor identification is a time-consuming task due to the large number of cones present within a single image; using the proposed FCN-based method could support the image analysis task, drastically reducing the need for manual assessment of the photoreceptor mosaic.