  Context: Carbon Enhanced Metal-Poor (CEMP) stars ($\mathrm{[C/Fe]} > 0.7$)
are known to exist in large numbers at low metallicity in the Milky Way halo
and are important tracers of early Galactic chemical evolution. However, very
few such stars have been identified in the classical dwarf spheroidal (dSph)
galaxies, and detailed abundances, including neutron-capture element
abundances, have only been reported for 12 stars. Aims: We aim to derive
detailed abundances of six CEMP stars identified in the Carina dSph and compare
the abundances to CEMP stars in other dSph galaxies and the Milky Way halo.
This is the largest sample of CEMP stars in a dSph galaxy analysed to date.
Methods: 1D LTE elemental abundances are derived via equivalent width and
spectral synthesis using high-resolution spectra of the six stars obtained with
the MIKE spectrograph at Las Campanas Observatory. Results: Abundances or upper
limits are derived for up to 27 elements from C to Os in the six stars. The
analysis reveals one of the stars to be a CEMP-no star with very low
neutron-capture element abundances. In contrast, the other five stars all show
enhancements in neutron-capture elements in addition to their carbon
enhancement, classifying them as CEMP-$s$ and -$r/s$ stars. The six stars have
similar $\alpha$ and iron-peak element abundances as other stars in Carina,
except for the CEMP-no star, which shows enhancement in Na, Mg, and Si. We
explore the absolute carbon abundances ($A(\rm C)$) of CEMP stars in dSph
galaxies and find similar behaviour as is seen for Milky Way halo CEMP stars,
but highlight that CEMP-$r/s$ stars primarily have very high $A(\rm C)$ values.
We also compare the neutron-capture element abundances of the CEMP-$r/s$ stars
in our sample to recent $i$-process yields, which provide a good match to the
derived abundances.
