  In this work, we investigate the form factors of $B_c$ decays into $J/\Psi,
\psi(2S,3S)$, $\eta_c, \eta_c(2S,3S), \chi_{c0}, \chi_{c1}, h_c$ and $X(3872)$
mesons in the covariant light-front quark model (CLFQM). For the purpose of the
branching ratio calculation, the form factors of $B_c\to D^{(*)}, D^{(*)}_s$
transitions are also included. In order to obtain the form factors for the
physical transition processes, we need extend these form factors from the
space-like region to the time-like region. The $q^2$-dependence for each
transition form factor is also plotted. Then, under the factorization method,
we calculate the branching ratios of 80 $B_c$ decay channels with a charmonium
involved in each mode. Most of our predictions are comparable with the results
given by most of other approaches. As to the decays with the radially excited
state S-wave charmonia, such as $\psi(2S,3S)$ and $\eta_c(2S,3S)$, involved,
there are two sets of parameters for their light-front wave functions,
corresponding to scenario I (SI) and scenario II (SII), are adopted to
calculate the branching ratios. Comparing with the future experimental data,
one can discriminate which parameters are more favored.
