COVID-19 is an infectious disease, which has adversely affected public health and the economy across the world. On account of the highly infectious nature of the disease, rapid automated diagnosis of COVID-19 is urgently needed. A few recent findings suggest that chest X-rays and CT scans can be used by machine learning for the diagnosis of COVID-19. Herein, we employed Semi-Supervised Learning (SSL) approaches to detect COVID-19 cases accurately by analyzing digital chest X-rays and CT scans. On a relatively small COVID-19 radiography dataset, which contains only 219 COVID-19 positive images, 1341 normal and 1345 viral pneumonia images, our algorithm, COVIDCon, which takes advantage of data augmentation, consistency regularization, and multicontrastive learning, attains 97.07% average class prediction accuracy, with 1000 labeled images, which is 7.65% better than the next best SSL method, Virtual Adversarial Training. COVIDCon performs even better on a larger COVID-19 CT Scan dataset that contains 82767 images. It achieved an excellent accuracy of 99.13%, at 20000 labels, which is 6.45% better than the next best Pseudo-Labeling approach. COVIDCon outperforms other state-of-the-art algorithms at every label that we have investigated. These results demonstrate COVIDCon as the benchmark SSL algorithm for potential diagnosis of COVID-19 from chest X-rays and CT-Scans. Furthermore, COVIDCon performs exceptionally well in identifying COVID-19 positive cases from a completely unseen repository with a confirmed COVID19 case history. COVIDCon, may provide a fast, accurate, and reliable method for screening COVID-19 patients.