We demonstrate laser cooling of trapped beryllium ions at 313 nm using a frequency-doubled extended cavity diode laser operated at 626 nm, obtained by cooling a ridge waveguide diode laser chip to -31°C. Up to 32 mW of narrowband 626 nm laser radiation is obtained. After passage through an optical isolator and beam shaping optics, 14 mW of 626 nm power remains of which 70% is coupled into an external enhancement cavity containing a nonlinear crystal for second-harmonic generation. We produce up to 35 μW of 313 nm radiation, which is subsequently used to laser cool and detect 6×10(2) beryllium ions, stored in a linear Paul trap, to a temperature of about 10 mK, as evidenced by the formation of Coulomb crystals. Our setup offers a simple and affordable alternative for Doppler cooling, optical pumping, and detection to presently used laser systems.