In a magnetic single electron transistor (SET), which consists of a magnetic quantum dot (QD) coupled electrically to nonmagnetic source, drain, and gate electrodes, a magnetic polaron (MP) formation may occur, that is, the charge carrier spin may spin-polarize the magnetic atoms of the QD and simultaneously the carrier becomes more tightly bound to the QD. We have studied theoretically the effect of the Coulomb interaction and magnetic field on the stability of the MPs in ferromagnetic SETs in the Coulomb blockade regime. The calculated results show that the temperature range, where MP is stable can be controlled by the gate voltage of the SET. At temperatures below the Curie temperature the stability decreases with magnetic field, whereas at higher temperatures the opposite is true. The Coulomb repulsion between two charge carriers separates the spin-up and spin-down energy levels, which stabilizes the MP further.