Over 100 μW of continuous-wave tunable ultraviolet radiation at 370 nm is generated by the sum-frequency mixing of radiation from two extended-cavity laser diodes having powers of 60 mW at 822 nm and 8 mW at 671 nm in a lithium iodate crystal. The crystal is placed in an external cavity that enhances the powers of two fundamental beams simultaneously by approximately 40. This light source is successfully applied to the laser cooling of trapped ytterbium ions.