We report the realization of a singly resonant optical parametric oscillator (SRO) that is designed to provide narrow-bandwidth, continuously tunable radiation at a wavelength of 1163 nm for optical cooling of osmium ions. The SRO is based on periodically poled, magnesium-oxide-doped lithium niobate and pumped at 532 nm. The output coupling of the resonant idler wave is adjusted to yield up to 400 mW of 1163 nm radiation, with a bandwidth of a few megahertz. For continuous frequency tuning of the idler wave, the SRO is equipped with an intracavity etalon, and the cavity length is controlled with a piezo-actuated mirror synchronized to the etalon angle.