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Context: We present COSTA (COld STream finder Algorithm), a novel algorithm to search for cold kinematical substructures in the phase space of planetary nebulae (PNe) and globular clusters (GCs) in the halo of massive galaxies and intracluster regions. Aims: COSTA aims at detecting small sized, low velocity dispersion streams, as the ones produced in recent interactions of dwarf galaxies with the halo of more massive galaxies, including the ones sitting in the central region of rich galaxy clusters. Methods: COSTA is based on a deep friend-of-friend procedure that isolates groups of N particles with small velocity dispersion (between 10 kms and $\sim$ 100 kms), using an iterative (n) sigma-clipping over a defined number of (k) neighbor particles. The algorithm has three parameters (k-n-N), plus a velocity dispersion cut-off, which defines the "coldness" of the stream, that are set using Montecarlo realizations of the sample under exam. Results: In this paper, we show the ability of COSTA to recover simulated streams on mock data-sets of discrete kinematical tracers with different sizes and measurement errors, from publicly available hydrodynamical simulations. We also show the best algorithm set-up for a realistic case of stream finding in the core of the Fornax cluster, for future applications of COSTA to real populations of PNe and GCs. Conclusions: COSTA can be generalized to all problems of finding small substructures in the phase space of a limited sample of discrete tracers, provided that the algorithm is trained on realistic mock observations reproducing the specific dataset under exam.