Recently, Epilepsy disorder has increasingly affected a large number of people worldwide, and it is a complex neurological condition characterized as recurrent, involuntary, paroxysmal seizure activity. Automated epilepsy diagnosis is vital to address the clinical gaps and impediments in epilepsy detection, prediction, and localization. Epilepsy diagnosis utilizes the EEG signals and adopts the Artificial Intelligence (AI) models to detect, predict, and localize seizure patterns in an automated manner. Even though deep neural networks have gained significant attention in epileptic seizure recognition, data scarcity is a primary constraint. Thus, this survey studies the emerging learning models that can address the scarcity of data on epilepsy diagnosis. In this context, to resolve the data scarcity, this work investigates the emerging learning models, including Few-shot Learning, Metric Learning, Self-Supervised Learning, Siamese Neural Networks, and Capsule Neural Networks. In particular, it reviews the epilepsy detection, prediction, and localization research works that address the data scarcity constraint on benchmark EEG datasets and possible solutions. Further, this survey concludes with research challenges, opportunities, and future research directions for building automated epilepsy diagnosis systems. As a result, this survey accentuates epilepsy researchers toward designing a reliable and robust epilepsy diagnosis model that efficiently works on EEG datasets with data scarcity.