Particle detectors at future collider experiments will operate at high collision rates and thus will have to face high pile up and a harsh radiation environment. Precision timing capabilities can help in the reconstruction of physics events by mitigating pile up effects. In this context, radiation tolerant, scintillating crystals coupled to silicon photomultipliers (SiPMs) can provide a flexible and compact option for the implementation of a precision timing layer inside large particle detectors. In this paper, we compare the timing performance of aluminum garnet crystals (YAG: Ce, LuAG: Ce, GAGG: Ce) and the improvements of their time resolution by means of codoping with Mg2+ ions. The crystals were read out using SiPMs from Hamamatsu glued to the rear end of the scintillator and their timing performance was evaluated by measuring the coincidence time resolution (CTR) of 150GeV charged pions traversing a pair of crystals. The influence of crystal properties, such as density, light yield and decay kinetics on the timing performance is discussed. The best single detector time resolutions are in the range of 23–30ps (sigma) and only achieved by codoping the garnet crystals with divalent ions, such as Mg2+. The much faster scintillation decay in the co-doped samples as compared to non co-doped garnets explains the higher timing performance. Samples of LSO: Ce, Ca and LYSO:Ce crystals have also been used as reference time device and showed a time resolution at the level of 17ps, in agreement with previous results.