We report both theoretical and numerical results on convection for a magnetic fluid under rotation in a viscoelastic carrier liquid. The viscoelastic properties are given by the Oldroyd model. We focus on the stationary convection for idealized boundary conditions. Close to the first bifurcation, the coefficients of the corresponding amplitude equation are determined. The effect of the Kelvin force and of the rotation on instability thresholds for a diluted suspension are also emphasized.