Context. Type II Cepheids (T2Ceps), alongside RR Lyrae stars, serve as important distance indicators for old Population II stars due to their period-luminosity (PL) relations. However, few studies of these relations in the Sloan photometric system have been conducted. Aims. Our goal is to calibrate PL relations (and their counterparts in Wesenheit magnitudes) in the Sloan-Pan-STARRS gP1rP1iP1 bands for Galactic T2Ceps located in the vicinity of the Sun. Methods. We collected data for 16 T2Ceps of the BL Her-type and 17 of the W Vir-type using 40 cm telescopes of the Las Cumbres Observatory Global Telescope Network. Geometric parallaxes were adopted from Gaia Data Release 3. Results. We have calibrated PL and period-Wesenheit relations for Milky Way BL Her and W Vir stars in the solar neighborhood, as well as for a combined sample of the two types. Conclusions. The relationships derived here will allow the determination of the distances to the T2Ceps that will be discovered by the Legacy Survey of Space and Time survey and, in turn, to probe the extended halo of the Milky Way, as well as the halos of nearby galaxies. To the best of our knowledge, the relations derived in this study are the first for Milky Way T2Ceps in the Sloan bands.