  ThCoC$_2$ is a non-BCS, noncentrosymmetric superconductor with $T_c \simeq
2.5$~K, in which pairing mechanism was suggested to be either spin fluctuations
or the electron-phonon coupling. Earlier experimental work revealed that $T_c$
can be greatly enhanced upon Ni doping in ThCo$_{1-x}$Ni$_x$C$_2$, up to 12~K
for $x = 0.4$. In this work, using the Korringa-Kohn-Rostoker method with the
coherent potential approximation (KKR-CPA), the evolution of the electronic
structure upon Ni doping was studied and the increase of the density of states
at the Fermi level was found. The electron-phonon coupling constant $\lambda$
was calculated using the rigid muffin tin approximation (RMTA) and the increase
in $\lambda(x)$ was found. This indirectly confirms the electron-phonon
coupling scenario as the trend in $\lambda(x)$ is in qualitative agreement with
the experiment when the electron-phonon pairing is assumed.
