We present Herschel PACS 100 and 160 mu m observations of the solar-type stars alpha Men, HD 88230 and HD 210277, which form part of the FGK stars sample of the Herschel open time key programme (OTKP) DUNES (DUst around NEarby S tars). Our observations show small infrared excesses at 160 mu m for all three stars. HD 210277 also shows a small excess at 100 mu m, while the 100 mu m fluxes of alpha Men and HD 88230 agree with the stellar photospheric predictions. We attribute these infrared excesses to a new class of cold, faint debris discs. Both alpha Men and HD 88230 are spatially resolved in the PACS 160 mu m images, while HD 210277 is point-like at that wavelength. The projected linear sizes of the extended emission lie in the range from similar to 115 to <= 250 AU. The estimated black body temperatures from the 100 and 160 mu m fluxes are less than or similar to 22 K, and the fractional luminosity of the cold dust is L-dust/L-* similar to 10(-6), close to the luminosity of the solar-system's Kuiper belt. These debris discs are the coldest and faintest discs discovered so far around mature stars, so they cannot be explained easily invoking "classical" debris disc models.