Point-contact spectroscopy was performed on single crystals of the heavy-fermion superconductor CeCoIn_5 between 150 mK and 2.5 K. A pulsed measurement technique ensured minimal Joule heating over a wide voltage range. The spectra show Andreev-reflection characteristics with multiple structures which depend on junction impedance. Spectral analysis using the generalized Blonder-Tinkham-Klapwijk formalism for d-wave pairing revealed two coexisting order parameter components, with amplitudes Delta_1 = 0.95 +/- 0.15 meV and Delta_2 = 2.4 +/- 0.3 meV, which evolve differently with temperature. Our observations indicate a highly unconventional pairing mechanism, possibly involving multiple bands.
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