We introduce a new distance determination method using carbon-rich asymptotic giant branch stars (CS) as standard candles and the Large and Small Magellanic Clouds (LMC and SMC) as the fundamental calibrators. We select the samples of CS from the ($(J-K_{s})_0$, $J_0$) colour-magnitude diagrams, as, in this combination of filters, CS are bright and easy to identify. We fit the CS $J$-band luminosity functions using a Lorentzian distribution modified to allow the distribution to be asymmetric. We use the parameters of the best-fit distribution to determine if the CS luminosity function of a given galaxy resembles that of the LMC or SMC. Based on this resemblance, we use either the LMC or SMC as the calibrator and estimate the distance to the given galaxy using the median $J$ magnitude ($overline{J}$) of the CS samples. We apply this new method to the two Local Group galaxies NGC 6822 and IC 1613. We find that NGC 6822 has an LMC-like CS luminosity function while IC 1613 is more SMC-like. Using the values for the median absolute $J$ magnitude for the LMC and SMC found in Paper I we find a distance modulus of $mu_{0}=23.54pm0.03$ (stat) for NGC 6822 and $mu_{0}=24.34pm0.05$ (stat) for IC 1613.
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