We present 21 new long-term variable radio sources found commensally in two years of weekly MeerKAT monitoring of the low-mass X-ray binary GX 339-4. The new sources vary on time scales of weeks to months and have a variety of light curve shapes and spectral index properties. Three of the new variable sources are coincident with multi-wavelength counterparts; and one of these is coincident with an optical source in deep MeerLICHT images. For most sources, we cannot eliminate refractive scintillation of active galactic nuclei as the cause of the variability. These new variable sources represent $2.2\pm0.5$ per cent of the unresolved sources in the field, which is consistent with the 1-2 per cent variability found in past radio variability surveys. However, we expect to find short-term variable sources in the field as well as these 21 new long-term variable sources. We present the radio light curves and spectral index variability of the new variable sources, as well as the absolute astrometry and matches to coincident sources at other wavelengths.