  Eccentricity tides generate a torque that can drive an ocean planet towards
asynchronous rotation states of equilibrium when enhanced by resonances
associated with the oceanic tidal modes. We investigate the impact of
eccentricity tides on the rotation of rocky planets hosting a thin uniform
ocean and orbiting cool dwarf stars such as TRAPPIST-1, with orbital periods
~1-10 days. Combining the linear theory of oceanic tides in the shallow water
approximation with the Andrade model for the solid part of the planet, we
develop a global model including the coupling effects of ocean loading,
self-attraction, and deformation of the solid regions. We derive from this
model analytic solutions for the tidal Love numbers and torque exerted on the
planet. These solutions are used with realistic values of parameters provided
by advanced models of the internal structure and tidal oscillations of solid
bodies to explore the parameter space both analytically and numerically. Our
model allows us to fully characterise the frequency-resonant tidal response of
the planet, and particularly the features of resonances associated with the
oceanic tidal modes (eigenfrequencies, resulting maxima of the tidal torque and
Love numbers) as functions of the planet parameters (mass, radius, Andrade
parameters, ocean depth and Rayleigh drag frequency). Resonances associated
with the oceanic tide decrease the critical eccentricity beyond which
asynchronous rotation states distinct from the usual spin-orbit resonances can
exist. We provide an estimation and scaling laws for this critical
eccentricity, which is found to be lowered by roughly one order of magnitude,
switching from ~0.3 to ~0.06 in typical cases and to ~0.01 in extremal ones.
