Theoretical calculations, computer simulations and experiments indicate the possible existence of a ferromagnetic liquid state. Should such a state exist, demagnetization effects would force a nontrivial magnetization texture governed by the shape of the liquid droplet. Since liquid droplets are deformable, the droplet shape couples to the magnetization texture. This paper solves the joint shape/texture problem subject to the assumption of cylindrical droplet symmetry. The shape undergoes a change in topology from spherical to toroidal as exchange energy grows or surface tension decreases.