  This is the second paper of a series exploring the multi-component (stars,
warm and cold gas and radio jets) properties of a sample of eleven nearby low
excitation radio galaxies (LERGs), with the aim of better understanding the AGN
fuelling/feedback cycle in these objects. Here we present a study of the
molecular gas kinematics of six sample galaxies detected in $^{12}$CO(2-1) with
ALMA. In all cases, our modelling suggests that the bulk of the gas in the
observed (sub-)kpc CO discs is in ordered rotation. Nevertheless, low-level
distortions are ubiquitous, indicating that the molecular gas is not fully
relaxed into the host galaxy potential. The majority of the discs, however, are
only marginally resolved, preventing us from drawing strong conclusions. NGC
3557 and NGC 3100 are special cases. The features observed in the CO velocity
curve of NGC 3557 allow us to estimate a super-massive black hole (SMBH) mass
of $(7.10\pm0.02)\times10^{8}$ M$_{\odot}$, in agreement with expectations from
the M$_{\rm SMBH}- \sigma_{*}$ relation. The rotation pattern of NGC 3100 shows
distortions that appear to be consistent with the presence of both a position
angle and inclination warp. Non-negligible radial motions are also found in the
plane of the CO disc, likely consistent with streaming motions associated with
the spiral pattern found in the inner regions of the disc. The dominant radial
motions are likely to be inflows, supporting a scenario in which the cold gas
is contributing to the fuelling of the AGN.
