  The total dust return rate from AGB and RSG star outflows is an important
constraint to galactic chemical evolution models. However, this requires
detailed radiative transfer (RT) modeling of individual stars, which becomes
impractical for large data sets. Another approach is to select the best-fit
spectral energy distribution (SED) from a grid of dust shell models, allowing
for a faster determination of the luminosities and mass-loss rates for entire
samples. We have developed the Grid of RSG and AGB ModelS (GRAMS) to measure
the mass-loss return from evolved stars. The models span the range of stellar,
dust shell and grain properties relevant to evolved stars. In this paper we
present the carbon-star grid and compare our results with data of Large
Magellanic Cloud (LMC) carbon stars from the SAGE and SAGE-Spec programs. We
generate spherically symmetric dust shell models using the 2Dust code, with
hydrostatic models for the central stars. We explore five values of the inner
radius R_in of the dust shell (1.5, 3, 4.5, 7 and 12 R_star). We use amorphous
carbon dust mixed with 10% silicon carbide by mass. The grain sizes follows a
KMH distribution. The models span 26 values of 11.3 um optical depth, ranging
from 0.001 to 4. For each model, 2Dust calculates the output SED from 0.2 to
200 um. Over 12,000 models have dust temperatures below 1800 K. The GRAMS
synthetic photometry is in good agreement with SAGE photometry for LMC
carbon-rich and extreme AGB star candidates, as well as spectroscopically
confirmed carbon stars from the SAGE-Spec study. Our models reproduce the IRAC
colors of most of the extreme AGB star candidates, consistent with the
expectation that a majority of these enshrouded stars have carbon-rich dust.
Finally, we fit the SEDs of some well-studied carbon stars and compare the
resulting luminosities and mass-loss rates with those from previous studies.
