In this work, we propose a novel Cyclic Image Translation Generative Adversarial Network (CIT-GAN) for multi-domain style transfer. To facilitate this, we introduce a Styling Network that has the capability to learn style characteristics of each domain represented in the training dataset. The Styling Network helps the generator to drive the translation of images from a source domain to a reference domain and generate synthetic images with style characteristics of the reference domain. The learned style characteristics for each domain depend on both the style loss and domain classification loss. This induces variability in style characteristics within each domain. The proposed CIT-GAN is used in the context of iris presentation attack detection (PAD) to generate synthetic presentation attack (PA) samples for classes that are under-represented in the training set. Evaluation using current state-of-the-art iris PAD methods demonstrates the efficacy of using such synthetically generated PA samples for training PAD methods. Further, the quality of the synthetically generated samples is evaluated using Frechet Inception Distance (FID) score. Results show that the quality of synthetic images generated by the proposed method is superior to that of other competing methods, including StarGan.