In order to detect and characterise cold extended circumstellar dust originating from collisions of planetesimal bodies in disks, belts, or rings at Kuiper-Belt distances (30-50 AU or beyond) sensitive submillimetre observations are essential. Measurements of the flux densities at these wavelengths will extend existing IR photometry and permit more detailed modelling of the Rayleigh-Jeans tail of the disks spectral energy distribution (SED), effectively constraining dust properties and disk extensions. By observing stars spanning from a few up to several hundred Myr, the evolution of debris disks during crucial phases of planet formation can be studied. We have performed 870-micron observations of 22 exo-Kuiper-Belt candidates, as part of a Large Programme with the LABOCA bolometer at the APEX telescope. Dust masses (or upper limits) were calculated from integrated 870-micron fluxes, and fits to the SED of detected sources revealed the fractional dust luminosities f_dust, dust temperatures T_dust, and power-law exponents beta of the opacity law. A total of 10 detections with at least 3-sigma significance were made, out of which five (HD 95086, HD 131835, HD 161868, HD 170773, and HD 207129) have previously never been detected at submillimetre wavelengths. Three additional sources are marginally detected with >2.5-sigma significance. The best-fit beta parameters all lie between 0.1 and 0.8, in agreement with previous results indicating the presence of grains that are significantly larger than those in the ISM. From our relatively small sample we estimate f_dust proportional to t^(-alpha), with alpha~0.8-2.0, and identify an evolution of the characteristic radial dust distance R_dust that is consistent with the t^(1/3) increase predicted from models of self-stirred collisions in debris disks.