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ABSTRACT The Planck-ATCA Coeval Observations (PACO) project collected data between 4.5 and 40 GHz for 482 sources selected within the Australia Telescope 20 GHz (AT20G) catalogue and observed with the Australia Telescope Compact Array. Observations were done almost simultaneously with the Planck satellite, in the period between 2009 July and 2010 August. In this paper, we present and discuss the data for the complete sample of 159 sources with SAT20G > 200 mJy in the South Ecliptic Pole region. The Planck Early Release Compact Source Catalogue (ERCSC) contains 57 of our sources. A comparison between the PACO catalogue and the ERCSC confirms that the reliability of the latter is better than 95 per cent. The missing ERCSC sources are typically associated with the Large Magellanic Cloud, the Milky Way or are otherwise extended. The spectral analysis of the PACO faint catalogue shows a spectral steepening of the sources at high frequencies, confirming the results obtained from the PACO bright sample. A comparison with AT20G measurements, carried out, on average, a few years earlier, has demonstrated that, on these time-scales, our sources show a rather high variability with an rms amplitude of ≃40 per cent at 20 GHz. The source spectral properties are found not to vary substantially with flux density, except for an increase in the fraction of steep spectrum sources at fainter flux densities. Our data also allow us to extend by a factor of ≃5 downwards in flux density the source counts at ≃33 and ≃40 GHz obtained from the ERCSC. This allows us to substantially improve our control on the contribution of unresolved extragalactic sources to the power spectrum of small-scale fluctuations in cosmic microwave background maps. [ABSTRACT FROM AUTHOR]