Relative risks have become a popular measure of treatment effect for binary outcomes in randomized controlled trials (RCTs). Relative risks can be estimated directly using log binomial regression but the model may fail to converge. Alternative methods are available for estimating relative risks but these have generally only been evaluated for independent data. As some of these methods are now being applied in cluster RCTs, investigation of their performance in this context is needed. We compare log binomial regression and three alternative methods (expanded logistic regression, log Poisson regression and log normal regression) for estimating relative risks in cluster RCTs. Clustering is taken into account using generalized estimating equations (GEEs) with an independence or exchangeable working correlation structure. The results of our large simulation study show that the log binomial GEE generally performs well for clustered data but suffers from convergence problems, as expected. Both the log Poisson GEE and log normal GEE have advantages in certain settings in terms of type I error, bias and coverage. The expanded logistic GEE can perform poorly and is sensitive to the chosen working correlation structure. Conclusions about the effectiveness of treatment often differ depending on the method used, highlighting the need to pre-specify an analysis approach. We recommend pre-specifying that either the log Poisson GEE or log normal GEE will be used in the event that the log binomial GEE fails to converge.