An all-coupling variational calculation has been performed to explore the formation and stability of a bipolaron in a polar semiconductor quantum dot. It has been shown that quantum confinement in general leads to a broadening of the bipolaron stability region. It has been furthermore shown for the first time that stable bipolarons can exist in realistic parabolic quantum dots of polar semiconductors like GaAs, CdS, CdTe and CdSe if they are fabricated in certain range of sizes.