We present solutions of the laminar compressible boundary-layer flows over the family of rotating cones subject to surface mass flux. The work is a generalization of previous studies of the compressible rotating-disk flow and incompressible rotating-cone flow without surface mass flux. Transformations are used which lead to a system of generalized von Kármán equations with boundary conditions parameterized by half-angle and a mass-flux parameter. Results are discussed in terms of wall temperature and local Mach number in the particular case of air, although the formulation is readily extended to other fluids. It is suggested that suction acts a stabilizing mechanism, whereas increased wall temperature and local Mach number have destabilizing influences.