We present Tails, an open-source deep-learning framework for the identification and localization of comets in the image data of the Zwicky Transient Facility (ZTF), a robotic optical time-domain survey currently in operation at the Palomar Observatory in California, USA. Tails employs a custom EfficientDet-based architecture and is capable of finding comets in single images in near real time, rather than requiring multiple epochs as with traditional methods. The system achieves state-of-the-art performance with 99% recall, 0.01% false positive rate, and 1-2 pixel root mean square error in the predicted position. We report the initial results of the Tails efficiency evaluation in a production setting on the data of the ZTF Twilight survey, including the first AI-assisted discovery of a comet (C/2020 T2) and the recovery of a comet (P/2016 J3 = P/2021 A3).