Cox PH assumes continuous time measurement, and would be inappropriate. If you have the same discrete time intervals for all subjects, using discrete time event history analysis (i.e., logit hazard, probit hazard, or complementary log-log hazard models) would be the way to go. I have included a list of approachable texts on the topic (there are many others). If you are using Stata, you might find the dthaz package useful, as it provides tools for handling the data and modeling requirements for discrete time event history models.
References
Singer, Judith D., & Willett, J. B. (1991). Modeling the days of our lives: Using survival analysis when designing and analyzing longitudinal studies of duration and the timing of events. Psychological Bulletin, 110(2), 268–290.
Singer, J. D., & Willett, J. B. (1993). It’s about time: Using discrete-time survival analysis to study duration and the timing of events. Journal of Educational and Behavioral Statistics, 18(2), 155–195.
Singer, J. D., & Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling change and event occurrence. Oxford University Press.