We present Herschel PACS 100 and 160 micron 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 micron for all three stars. HD 210277 also shows a small excess at 100 micron, while the 100 micron 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. alpha Men and HD 88230 are spatially resolved in the PACS 160 micron images, while HD 210277 is point-like at that wavelength. The projected linear sizes of the extended emission lie in the range from ~ 115 to ~ 250 AU. The estimated black body temperatures from the 100 and 160 micron fluxes are $lesssim$ 22 K, while the fractional luminosity of the cold dust is Ldust/Lstar ~ 10E-6, close to the luminosity of the Solar-Systems Kuiper belt. These debris discs are the coldest and faintest discs discovered so far around mature stars and cannot easily be explained by invoking classical debris disc models.