Recently, the rapid advancements in Deep Learning and Computer Vision technologies have introduced a new and exciting era in the field of skin disease analysis. However, there are certain challenges in the roadmap towards developing such technologies for real-life applications that must be investigated. This study considers one of the key challenges in data acquisition and computation, viz. data scarcity. Data scarcity is a central problem in acquiring medical images and applying machine learning techniques to train Convolutional Neural Networks for disease diagnosis. The main objective of this study is to explore the possible methods to deal with the data scarcity problem and to improve diagnosis with small datasets. The challenges in data acquisition for a few lamentably neglected skin conditions such as rosacea are an excellent instance to explore the possibilities of improving computer-aided skin disease diagnosis. With data scarcity in mind, the possible techniques explored and discussed include Generative Adversarial Networks, Meta-Learning, Few-Shot classification, and 3D face modelling. Furthermore, the existing studies are discussed based on skin conditions considered, data volume and implementation choices. Some future research directions are recommended.