Analysis of kinship from facial images or videos is an important problem. Prior machine learning and computer vision studies approach kinship analysis as a verification or recognition task. In this paper, first time in the literature, we propose a kinship synthesis framework, which generates smile videos of (probable) children from the smile videos of parents. While the appearance of a child's smile is learned using a convolutional encoder-decoder network, another neural network models the dynamics of the corresponding smile. The smile video of the estimated child is synthesized by the combined use of appearance and dynamics models. In order to validate our results, we perform kinship verification experiments using videos of real parents and estimated children generated by our framework. The results show that generated videos of children achieve higher correct verification rates than those of real children. Our results also indicate that the use of generated videos together with the real ones in the training of kinship verification models, increases the accuracy, suggesting that such videos can be used as a synthetic dataset.