Continual learning (CL) in the context of Generative Adversarial Networks (GANs) remains a challenging problem, particularly when it comes to learn from a few-shot (FS) samples without catastrophic forgetting. Current most effective state-of-the-art (SOTA) methods, like LFS-GAN, introduce a non-negligible quantity of new weights at each training iteration, which would become significant when considering the long term. For this reason, this paper introduces \textcolor{red}{\textbf{\underline{c}}}ontinual few-sh\textcolor{red}{\textbf{\underline{o}}}t learning with \textcolor{red}{\textbf{\underline{lo}}}w-\textcolor{red}{\textbf{\underline{r}}}ank adaptation in GANs named CoLoR-GAN, a framework designed to handle both FS and CL together, leveraging low-rank tensors to efficiently adapt the model to target tasks while reducing even more the number of parameters required. Applying a vanilla LoRA implementation already permitted us to obtain pretty good results. In order to optimize even further the size of the adapters, we challenged LoRA limits introducing a LoRA in LoRA (LLoRA) technique for convolutional layers. Finally, aware of the criticality linked to the choice of the hyperparameters of LoRA, we provide an empirical study to easily find the best ones. We demonstrate the effectiveness of CoLoR-GAN through experiments on several benchmark CL and FS tasks and show that our model is efficient, reaching SOTA performance but with a number of resources enormously reduced. Source code is available on \href{https://github.com/munsifali11/CoLoR-GAN}{Github.