  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 disks typically regarded as circumstellar
rather than circumbinary, including AB Aurigae and HD 100546.
