We report the results of a radio monitoring program conducted at the Australia Telescope Compact Array to search for quiescent and flaring emission from seven nearby Southern late-type M and L dwarfs. Two late-type M dwarfs, the M7 V LHS 3003 and the M8 V DENIS 1048-3956, were detected in quiescent emission at 4.80 GHz. The observed emission is consistent with optically thin gyrosynchrotron emission from mildly relativistic (~1-10 keV) electrons with source densities n_e <~ 10^9 cm^-3 in B >~

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... G magnetic fields. DENIS 1048-3956 was also detected in two spectacular, short-lived flares, one at 4.80 GHz (peak f_nu = 6.0+/-0.8 mJy) and one at 8.64 GHz (peak f_nu = 29.6+/-1.0 mJy) approximately 10 minutes later. The high brightness temperature (T_B >~ 10^13 K), short emission period (~4-5 minutes), high circular polarization (~100%), and apparently narrow spectral bandwidth of these events imply a coherent emission process in a region of high electron density (n_e ~ 10^11-10^12 cm^-3) and magnetic field strength (B ~ 1 kG). If the two flare events are related, the apparent frequency drift in the emission suggests that the emitting source either moved into regions of higher electron or magnetic flux density; or was compressed, e.g., by twisting field lines or gas motions. The quiescent fluxes from the radio-emitting M dwarfs violate the Gudel-Benz empirical radio/X-ray relations, confirming a trend previously noted by Berger et al. (abridged)