We report the development of a fiber-integrated picosecond source at 560 nm by second harmonic generation of a Raman fiber laser. A picosecond ytterbium master oscillator power fiber amplifier is used to pulse-pump a Raman amplifier, which is seeded by a continuous wave distributed feedback laser diode operating at 1120 nm. The pulse train generated at 1120 nm is frequency-doubled in a fiber-coupled periodically-poled lithium niobate crystal module, producing 450 mW of average power at 560 nm with a pulse duration of 150 ps at a repetition rate of 47.5 MHz. The near diffraction-limited (M2 = 1.02) collimated output beam is ideal for super-resolution microscopy applications.