By their very nature, recommendation systems that are based on the analysis of personal data are prone to leak information about personal preferences. In online dating, that data might be highly personal. The goal of this work is to analyse, for different online dating recommendation systems from the literature, if differential privacy can be used to hide individual connections (for example, an expression of interest) in the data set from any other user on the platform - or an adversary that has access to the information of one or multiple users. We investigate two recommendation systems from the literature on their potential to be modified to satisfy differential privacy, in the sense that individual connections are hidden from anyone else on the platform. For Social Collab by Cai et al. we show that this is impossible, while for RECON by Pizzato et al. we give an algorithm that theoretically promises a good trade-off between accuracy and privacy. Further, we consider the problem of stochastic matching, which is used as the basis for some other recommendation systems. Here we show the possibility of a good accuracy and privacy trade-off under edge-differential privacy.