  We develop and test a method for the estimation of metallicities ([Fe/H]) and
carbon abundance ratios ([C/Fe]) for carbon-enhanced metal-poor (CEMP) stars,
based on application of artificial neural networks, regressions, and synthesis
models to medium-resolution (1-2 A) spectra and J-K colors. We calibrate this
method by comparison with metallicities and carbon abundance determinations for
118 stars with available high-resolution analyses reported in the recent
literature. The neural network and regression approaches make use of a
previously defined set of line-strength indices quantifying the strength of the
CaII K line and the CH G-band, in conjuction with J-K colors from the 2MASS
Point Source Catalog. The use of near-IR colors, as opposed to broadband B-V
colors, is required because of the potentially large affect of strong molecular
carbon bands on bluer color indices. Using these methods we are able to
reproduce the previously-measured [Fe/H] and [C/Fe] determinations with an
accuracy of ~ 0.25 dex for stars in the metallicity interval -5.5 <= [Fe/H]} <=
-1.0, and with 0.2 <= (J-K)o <= 0.8. At higher metallicity the CaII K line
begins to saturate, especially for the cool stars in our program, hence this
approach is not useful in some cases. As a first application, we estimate the
abundances of [Fe/H] and [C/Fe] for the 56 stars identified as possibly
carbon-rich, relative to stars of similar metal abundance, in the sample of
"strong G-band" stars discussed by Beers, Preston, & Shectman. (abridged)
