We present Spitzer/IRAC observations of dust formation from six extragalactic carbon-rich Wolf-Rayet (WC) binary candidates in low-metallicity (Z $lesssim0.65$ Z$_odot$) environments using multi-epoch mid-infrared (IR) imaging data from the SPitzer InfraRed Intensive Transients Survey (SPIRITS). Optical follow-up spectroscopy of SPIRITS~16ln, 19q, 16df, 18hb, and 14apu reveals emission features from C IV $lambda5801text{-}12$~and/or the C III-IV $lambda4650$ He II $lambda4686$~blend that are consistent with early-type WC stars. We identify SPIRITS~16ln as the variable mid-IR counterpart of the recently discovered colliding-wind WC4+O binary candidate, N604-WRXc, located in the sub-solar metallicity NGC 604 H II~region in M33. We interpret the mid-IR variability from SPIRITS~16ln as a dust-formation episode in an eccentric colliding-wind WC binary. SPIRITS~19q, 16df, 14apu, and 18hb exhibit absolute [3.6] magnitudes exceeding one of most IR-luminous dust-forming WC systems known, WR~104 (M$_mathrm{[3.6]}lesssim-12.3$). An analysis of dust formation in the mid-IR outburst from SPIRITS~19q reveals a high dust production rate of $dot{M}_dgtrsim2times10^{-6}$ M$_odot$ yr$^{-1}$, which may therefore exceed that of the most efficient dust-forming WC systems known. We demonstrate that efficient dust-formation is feasible from early-type WC binaries in the theoretical framework of colliding-wind binary dust formation if the systems host an O-type companion with a high mass-loss rate ($dot{M}gtrsim1.6times10^{-6}$ M$_odot$ yr$^{-1}$). This efficient dust-formation from early-type WC binaries highlights their potential role as significant sources of dust in low-metallicity environments.
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