  A complex structure of the superconducting order parameter in $Ln_2$C$_3$
($Ln$ = La, Y) is demonstrated by muon spin relaxation ($\mu$SR) measurements
in their mixed state. The muon depolarization rate [$\sigma_{\rm v}(T)$]
exhibits a characteristic temperature dependence that can be perfectly
described by a phenomenological double-gap model for nodeless
superconductivity. While the magnitude of two gaps is similar between
La$_2$C$_3$ and Y$_2$C$_3$, a significant difference in the interband coupling
between those two cases is clearly observed in the behavior of $\sigma_{\rm
v}(T)$.
