Recent studies of faint high-latitude carbon stars have shown that a significant fraction of them are not distant asymptotic giant branch (AGB) stars but rather belong to the local population of spheroid dwarfs. In this paper we attempt a theoretical prediction of the local space density of such dwarf carbon stars (dCs), based on the assumption that they are ordinary main-sequence stars that were able to accrete enough carbon- enriched material from a binary companion on the AGB to make their C/O ratio larger than unity.A simulated population of dCs is constructed by following the evolution of a large number of binaries using simple analytic fits to detailed evolutionary calculations and determining which ones would presently contain a dC. The zero-age parameters of the sample are chosen randomly from distributions derived from the observed properties of unevolved binaries. The space density of halo dCs that we predict (∼2-4 × 10-7 pc-3) is in agreement with current observational constraints. The predicted local space density of disk dCs (∼1 × 10-6 pc-3) may be somewhat higher than observed. The fraction of binaries that produces dCs depends strongly on initial metallicity and virtually no dCs are formed in systems with an initial metallicity of more than half solar. Thus, all disk dCs are predicted to be in binaries that formed in the very early phases of disk star formation, and their number depends strongly on assumptions about the age-metallicity relation during this epoch. The predictions for the halo are much less model-dependent. The simulated orbital period distributions are bimodal, with one peak between 103 and 105 days and another peak between 102 and 103 days. The shorter period component is caused by systems that have gone through a common envelope phase. The simulated period distributions bear a strong resemblance to the observed orbital period distribution of barium and CH giants, which may be the evolved descendants of the disk and halo dC populations we have modeled.