Pairwise likelihood methods are commonly used for inference in parametric statistical models in cases where the full likelihood is too complex to be used, such as multivariate count data. Although pairwise likelihood methods represent a useful solution to perform inference for intractable likelihoods, several computational challenges remain, particularly in higher dimensions. To alleviate these issues, we consider a randomized pairwise likelihood approach, where only summands randomly sampled across observations and pairs are used for the estimation. In addition to the usual tradeoff between statistical and computational efficiency, we show that, under a condition on the sampling parameter, this two-way random sampling mechanism allows for the construction of less computationally expensive confidence intervals. The proposed approach, which is implemented in the rpl R package, is illustrated in tandem with copula-based models for multivariate count data in simulations and on a set of transcriptomic data.