We report a narrowband and tunable diamond Raman laser generating eye-safe radiation suitable for water vapor detection. Frequency conversion of a tunable pump laser operating from 1063 to 1066 nm to the second order Stokes component in an external standing-wave cavity yielded 7 W of multimode output power in the wavelength range from 483 to 1488 nm at a conversion efficiency of 21%. Stable single longitudinal mode operation was achieved over the whole tuning range at low power (0.1 W), whereas incorporation of a volume Bragg grating as an output coupler enabled much higher stable power to be attained (0.5 W). A frequency stability of 40 MHz was obtained over a minute without active cavity stabilization. It was found that mode stability is aided via seeding of the second Stokes by four-wave mixing, which leads to a doubling of the mode-hopping interval. The laser was employed for the detection of water vapor in ambient air, demonstrating its potential for remote sensing applications.