We report an all-fiber pulsed source based on parametric conversion followed by thulium amplification able to deliver picosecond pulses at a repetition rate selectable between 2 and 5 GHz, of which central wavelength can be freely selected in the 2 micron region. A very versatile Nyquist pulse shaping of the parametric pump, which allows for the electrical control of the pulse train, enables such a freedom in the repetition rate selection, as well as some control in the pulse duration. We also show that data can be embedded in the output pulse train resulting in a high quality Gb/s return-to-zero transmitter. Such a programmable short-wave infrared laser is of high interest for sensing or nonlinear optics applications around 2000 nm that require a fine adjustment in both the spectral and temporal domains.