We perform two-dimensional particle-in-cell simulations of reconnection in magnetically dominated electron-positron plasmas subject to strong Compton cooling. We vary the magnetization $sigmagg1$, defined as the ratio of magnetic tension to plasma inertia, and the strength of cooling losses. Magnetic reconnection under such conditions can operate in magnetically dominated coronae around accreting black holes, which produce hard X-rays through Comptonization of seed soft photons. We find that the particle energy spectrum is dominated by a peak at mildly relativistic energies, which results from bulk motions of cooled plasmoids. The peak has a quasi-Maxwellian shape with an effective temperature of $sim 100$ keV, which depends only weakly on the flow magnetization and the strength of radiative cooling. The mean bulk energy of the reconnected plasma is roughly independent of $sigma$, whereas the variance is larger for higher magnetizations. The spectra also display a high-energy tail, which receives $sim 25$% of the dissipated reconnection power for $sigma=10$ and $sim 40$% for $sigma=40$. We complement our particle-in-cell studies with a Monte-Carlo simulation of the transfer of seed soft photons through the reconnection layer, and find the escaping X-ray spectrum. The simulation demonstrates that Comptonization is dominated by the bulk motions in the chain of Compton-cooled plasmoids and, for $sigmasim 10$, yields a spectrum consistent with the typical hard state of accreting black holes.
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