Generative Adversarial Networks (GANs) are deep learning architectures capable of generating synthetic datasets. Despite producing high-quality synthetic images, the default GAN has no control over the kinds of images it generates. The Information Maximizing GAN (InfoGAN) is a variant of the default GAN that introduces feature-control variables that are automatically learned by the framework, hence providing greater control over the different kinds of images produced. Due to the high model complexity of InfoGAN, the generative distribution tends to be concentrated around the training data points. This is a critical problem as the models may inadvertently expose the sensitive and private information present in the dataset. To address this problem, we propose a differentially private version of InfoGAN (DP-InfoGAN). We also extend our framework to a distributed setting (DPD-InfoGAN) to allow clients to learn different attributes present in other clients' datasets in a privacy-preserving manner. In our experiments, we show that both DP-InfoGAN and DPD-InfoGAN can synthesize high-quality images with flexible control over image attributes while preserving privacy.