The Beta Pictoris Moving Group is a nearby stellar association of young (12Myr) co-moving stars including the classical debris disk star beta Pictoris. Due to their proximity and youth they are excellent targets when searching for submillimetre emission from cold, extended, dust components produced by collisions in Kuiper-Belt-like disks. They also allow an age independent study of debris disk properties as a function of other stellar parameters. We observed 7 infrared-excess stars in the Beta Pictoris Moving Group with the LABOCA bolometer array, operating at a central wavelength of 870 micron at the 12-m submillimetre telescope APEX. The main emission at these wavelengths comes from large, cold dust grains, which constitute the main part of the total dust mass, and hence, for an optically thin case, make better estimates on the total dust mass than earlier infrared observations. Fitting the spectral energy distribution with combined optical and infrared photometry gives information on the temperature and radial extent of the disk. From our sample, beta Pic, HD181327, and HD172555 were detected with at least 3-sigma certainty, while all others are below 2-sigma and considered non-detections. The image of beta Pic shows an offset flux density peak located near the south-west extension of the disk, similar to the one previously found by SCUBA at the JCMT. We present SED fits for detected sources and give an upper limit on the dust mass for undetected ones. We find a mean fractional dust luminosity f_dust=11x10^{-4} at t=12Myr, which together with recent data at 100Myr suggests an f_dust propto t^{-alpha} decline of the emitting dust, with alpha > 0.8.