We have studied the spin structure of circular four-electron quantum rings using tunable confinement potentials. The calculations were done using the exact diagonalization method. Our results indicate that ringlike systems can have oscillatory flips between ferromagnetic and antiferromagnetic behaviour as a function of the magnetic field. Furthermore, at constant external magnetic fields there were seen similar oscillatory changes between ferromagnetism and antiferromagnetism when the system parameters were changed. Ackording to our results, the magnetism of quantum rings could be tuned by system parameters.We have studied the spin structure of circular four-electron quantum rings using tunable confinement potentials. The calculations were done using the exact diagonalization method. Our results indicate that ringlike systems can have oscillatory flips between ferromagnetic and antiferromagnetic behaviour as a function of the magnetic field. Furthermore, at constant external magnetic fields there were seen similar oscillatory changes between ferromagnetism and antiferromagnetism when the system parameters were changed. According to our results, the magnetism of quantum rings could be tuned by system parameters. ; Comment: 5 pages, 3 figures, article. Typo corrected