If you want a direct measurement you could look into electron spin resonance (ESR, only measures paramagnetic defects) or modulated photocurrent spectroscopy. Both are somewhat complex. SCLC, which Prof. Shukla proposed, is simpler and works too, provided SCLC is the dominant conduction mechanism.
No particular method of DOS determination is suitable for all chalcogenide glasses. If you can make schottky barrier or p- n junction, DLTS and other junction spectroscopies can be used. If you can not make such devices then constant photocurrent method, thermally stimulated current method can be used but sample should be highly photoconducting. SCLC can be used provided sample is quite insulating. In conclusion, method is dependent on the glassy system used.As the defects are not unpaired in ordinary situation, ESR signal is not observed and hence EPR method can not be used in chalcogenide glasses.