We re-evaluate the fluxes of cosmic ray antiprotons, positrons and gamma rays to be expected from the annihilations of relic particles in the galactic halo. We stress the importance of observational constraints on the possible halo density of relic particles, and specify their annihilation cross sections by the requirement that their cosmological density close the Universe. We use a Monte Carlo programme adapted to fit e+e- data to calculate the p̄, e+ and γ spectra for some supersymmetric relic candidates. We find significantly smaller p̄ fluxes than previously estimated, and conclude that present upper limits on cosmic ray p̄ and e+ do not exclude any range of sparticle masses. We discuss the prospects for possible future constraints on sparticles from cosmic γ rays.