Context : Previous observations with the Infrared Astronomical Satellite and the Infrared Space Observatory , and ongoing observations with Spitzer and AKARI have led to the discovery of over 200 debris disks , based on detected mid- and far infrared excess emission , indicating warm circumstellar dust . In order to constrain the properties of these systems , e.g. , to more accurately determine the dust mass , temperature and radial extent , follow-up observations in the submillimetre wavelength region are needed . Aims : The \beta Pictoris Moving Group is a nearby stellar association of young ( { \sim } 12 Myr ) 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 . Methods : We observed 7 infrared-excess stars in the \beta Pictoris Moving Group with the LABOCA bolometer array , operating at a central wavelength of 870 \mu m 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 . Results : From our sample , \beta Pic , HD 181327 , and HD 172555 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 . Conclusions : We find a mean fractional dust luminosity \bar { f } _ { \mathrm { dust } } = 11 { \cdot } 10 ^ { -4 } at t \approx 12 Myr , which together with recent data at 100 Myr suggests an f _ { \mathrm { dust } } \propto t ^ { - \alpha } decline of the emitting dust , with { \alpha } > 0.8 .