We present the ground work for a model that can be used for the generation of postage stamp images of sythetic radio sources in the Fanaroff Riley Class I (FRI) and Class II (FRII). These can be used in the simulation of radio surveys like the square kilometre array. We make use of a variational auto-encoder (VAE) that consists of two fully connected networks, an encoder and a decoder. In the first phase, we trained an unsupervised variational auto-encoder. The network was trained using postage stamp images from the Faint images of the radio sky at twenty-centimetres. We optimised the latent space of the auto-encoder and introduce the radio morphology inception score (RAMIS) to quantitatively evaluate the performance of the network. We also examined the self-organizing ability of the VAE by using a 2-dimensional latent space and we discuss how this can be used to control the synthetic radio sources. In a second phase, we made use of the conditional variational autoencoder (CVAE), which is a supervised version of the VAE, the network was trained by taking into account the FRI and FRII labels of the train images. We again made use of the RAMIS to quantify the quality of the images and also evaluate the class generation efficiency of the network by classifying the generated images using existing convolutional neural networks classifiers. We finally found that the best model was obtained for the network with latent dimensions d = 32 trained for 5000 epochs where a RAMIS of 1.17 was obtained, 1.4 being that of an ideal radio source generative model.