We demonstrate a high-efficiency continuous-wave (CW) diamond Raman laser operating at 1178 nm with enhanced stability by using a V-cavity design. A maximum Stokes power of 39 Wwith a conversion efficiency of 45% was achieved using a linearly-polarized 1018 nm Yb-doped fiber pump laser. The Stokes CW power stability showed superior stability over a linear cavity when characterized over periods up to 15 min. The Stokes output was found to switch between linear, elliptical, and random polarization with varying pump polarization. The results represent a major step towards stable, efficient and high-power CW lasers at 1178 nm and at wavelengths outside the main Yb, and Nd emission bands.