  We present a solid-state laser system that generates over 200 mW of
continuous-wave, narrowband light, tunable from 316.3 nm - 317.7 nm and 318.0
nm - 319.3 nm. The laser is based on commercially available fiber amplifiers
and optical frequency doubling technology, along with sum frequency generation
in a periodically poled stoichiometric lithium tantalate crystal. The laser
frequency is stabilized to an atomic-referenced high finesse optical transfer
cavity. Using a GPS-referenced optical frequency comb we measure a long term
frequency instability of $<$35 kHz for timescales between $10^{-3}$ s and
$10^3$ s. As an application we perform spectroscopy of Sr Rydberg states from
$n$ = 37 - 81, demonstrating mode-hop-free scans of 24 GHz. In a cold atomic
sample we measure Doppler-limited linewidths of 350 kHz.
