Kinematic studies of protoplanetary discs are a valuable method for uncovering hidden companions. In the first paper of this series, we presented five morphological and kinematic criteria that aid in asserting the binary nature of a protoplanetary disc. In this work, we study the kinematic signatures of circumbinary discs in the residuals of their velocity maps. We show that Doppler-flips, spiral arms, eccentric gas motion, fast flows inside of the cavity, and vortex-like kinematic signatures are commonly observed. Unlike in the planetary mass companion case, Doppler-flips in circumbinary discs are not necessarily centred on a companion, and can extend towards the cavity edge. We then compare the kinematic signatures in our simulations with observations and see similarities to the Doppler-flip signal in HD 100546 and the vortex-like kinematic signatures in HD 142527. Our analysis also reveals kinematic evidence for binarity in several protoplantary discs typically regarded as circumstellar rather than circumbinary, including AB Aurigae and HD 100546.