Motivated by the problems of magnetic flux storage and dynamo action in stars with convection zones, we study the equilibrium and stability of magnetic flux tubes under the influence of differential rotation and stratification. The formalism developed in the first paper in this series is applied to axisymmetric, toroidal flux tubes (flux rings) lying in planes parallel to the equator at an arbitrary latitude. We assume mechanical force equilibrium, which requires neutral buoyancy of the flux tube and a longitudinal internal flow in the direction of stellar rotation. Stability against isentropic perturbations is investigated by considering both axisymmetric and non-axisymmetric, three-dimensional displacements of the equilibrium configuration. For axisymmetric modes, we find qualitative differences between the stability criteria for flux tubes within and outside the equatorial plane, where instability is generally easier to excite and overstable modes appear. In the case of non-axisymmetric perturbations, the results of a numerical study with parameter values corresponding to the bottom of the solar convection zone are discussed. The stability properties depend in a complicated way on the various parameters (e.g., latitude, magnetic field, superadiabaticity of the stratification, angular velocity and its gradient). While the magnetic field value for the onset of undulatory (Parker) instability with large growth rates is mainly determined by the stratification and the rotation rate, instabilities at somewhat lower field strengths with relatively small growth rates depend strongly on the sign and the value of the angular velocity gradient.