We report the generation of tunable continuous-wave (cw) mid-infrared (mid-IR) radiation across 4608-4694 nm using the new nonlinear material, orientation-patterned gallium phosphide (OP-GaP). By exploiting difference-frequency mixing between a cw Tm-fiber laser and a home-built cw optical parametric oscillator in a 40-mm-long crystal, we have generated up to 43 mW of cw output power, with >30 mW across >95% of the mid-IR tuning range. The output at 4608 nm exhibits high beam quality with a passive power stability of 2.5% rms over 1.5 min. The temperature acceptance bandwidth of the OP-GaP crystal has been measured and compared with theory. The performance of the mid-IR source at high pump powers and polarization-dependent transmission in OP-GaP has been investigated.