Opportunistic communications have been recently proposed as a key strategy for offloading traffic from 3G/4G cellular networks, which is particularly beneficial in case of crowded areas where many users are interested in similar contents. To conserve energy, duty cycling schemes are typically applied, and therefore contacts between nodes may become intermittent and sporadic also in dense networks. It is thus of paramount importance to accurately tune the duty cycling policy in order to meet energy requirements without compromising the quality of communications. In this paper, building upon a model of duty cycling in opportunistic networks that we have validated in a previous work, we study how to optimise the value of the duty cycle in order to provide probabilistic guarantees on the delay experienced by messages. More specifically, for a broad range of end-to-end delay distributions, we provide closed-form approximated solutions for deriving the optimal duty cycle such that the probability that the delay is smaller than a target value z is greater than or equal to a configurable probability p.