Your question is close to [this one](https://stats.stackexchange.com/questions/82720/confidence-interval-around-binomial-estimate-of-0-or-1/82724#82724) about constructing confidence limits when the binomial estimate is either zero or one. But you have multiple users, and want to estimate a small probability for each one. 

Then, if you are willing to assume this small probabilities are similar (your users are *exchangeable* in this regard), you can get strength from using all the data at once. In some way you could estimate one common $p$, and then the individual estimates could be shrinked towards this common estimate. That could be done in a Bayesian or empirical Bayesian way. This is also called a hierarchical bayes model.