We report on a systematic study of the Coulomb-blockade effects in nanofabricated narrow constrictions in thin (Ga,Mn)As films. Different low-temperature transport regimes have been observed for decreasing constriction sizes: the Ohmic, the single-electron tunneling (SET), and a completely insulating regime. In the SET, complex stability diagrams with nested Coulomb diamonds and anomalous conductance suppression in the vicinity of charge degeneracy points have been observed. We rationalize these observations in the SET with a double ferromagnetic island model coupled to ferromagnetic leads. Its transport characteristics are analyzed in terms of a modified orthodox theory of Coulomb blockade which takes into account the energy dependence of the density of states in the metallic islands.