Accurate values for the viscosity of the radioactive hydrogen isotope tritium (T2) at cryogenic temperatures are unavailable. Values for tritium found in literature are based on extrapolation by mass ratios as well as an empirical factor derived from hydrogen (H2) and deuterium (D2) viscosity measurements, or classical kinetic theory which does not handle quantum effects. Accurate data of the tritium viscosity will help to improve the modelling of the viscosity of diatomic molecules and can be used as a test of their interaction potentials.With this contribution we report a major step towards a fully tritium and cryogenic temperature compatible setup for the accurate measurement of the viscosity of gases, using a spinning rotor gauge (SRG) at the Tritium Laboratory Karlsruhe. After calibration with helium, measurements with hydrogen and deuterium conducted at room temperature agree with literature values within 2%. The performance at liquid nitrogen (LN2) temperature has been successfully demonstrated with a second setup in a liquid nitrogen bath. Again after calibration with helium at LN2 temperature, the viscosities of H2 and D2 were determined and are in agreement with literature to about 2%.