The article explores different deep convolutional neural network architectures trained and tested on posteroanterior chest X-rays of 327 patients who are healthy (152 patients), diagnosed with COVID-19 (125), and other types of pneumonia (48). In particular, this paper looks at the deep convolutional neural networks VGG16 and VGG19, InceptionResNetV2 and InceptionV3, as well as Xception, all followed by a flat multi-layer perceptron and a final 30% drop-out. The paper has found that the best performing network is VGG16 with a final $30$% drop-out trained over 3 classes (COVID-19, No Finding, Other Pneumonia). It has an internal cross-validated accuracy of $93.9(\pm3.4)$%, a COVID-19 sensitivity of $87.7(-1.9,+2)$%, and a No Finding sensitivity of $96.8(\pm0.8)$%. The respective external cross-validated values are $84.1(\pm13.5)$%, $87.7(-1.9,2)$%, and $96.8(\pm0.8)$%. The model optimizer was Adam with a 1e-4 learning rate, and categorical cross-entropy loss. It is hoped that, once this research will be put to practice in hospitals, healthcare professionals will be able in the medium to long-term to diagnosing through machine learning tools possible pneumonia, and if detected, whether it is linked to a COVID-19 infection, allowing the detection of new possible COVID-19 foyers after the end of possible "stop-and-go" lockdowns as expected by until a vaccine is found and widespread. Furthermore, in the short-term, it is hoped practitioners can compare the diagnosis from the deep convolutional neural networks with possible RT-PCR testing results, and if clashing, a Computed Tomography could be performed as they are more accurate in showing COVID-19 pneumonia.