The extra low-energy antiproton ring (ELENA) is a CERN particle decelerator with the purpose to deliver antiprotons at lowest energies aiming to enhance the study of antimatter. The hexagonal shaped ring with a circumference of about 30 m will decelerate antiprotons from momenta of 100 to 13.7 MeV=c. In this paper, the design approach for a magnet system for such a machine is presented. Due to the extra-low beam rigidity, the design of the magnet system is especially challenging because even small fields, arising for example from residual magnetization and hysteresis, have a major impact on beam dynamics. In total, seven prototype magnets of three different magnet types have been built and tested. This paper outlines challenges, describes solutions for the design of the magnet system and discusses the results of the prototypes.