  We study the exclusive two-body nonleptonic $B_c\to X_{c\bar{c}}M$ decays,
where $X_{c\bar{c}}$ is either a ground(1S) or a radially excited (2S or 3S)
charmonium and $M$ is a pseudoscalar $(P)$ or a vector $(V)$ meson. We consider
here three categories of decays: $B_c \to PP, PV, VP$ decays within the
framework of relativistic independent quark(RIQ) model based on a
flavor-independent interaction potential in scalar-vector harmonic form. Using
the factorization approximation, we calculate the weak form factors from the
overlapping integrals of meson wave functions obtained in the RIQ model and
predict the branching fractions for a set of exclusive nonleptonic $B_c$-decays
in reasonable agreement with other model predictions. Some of the decays of
interest are found to have branching fractions $\sim (10^{-3}-10^{-4})$ within
the detection ability of the current experiments and can be precisely measured
at LHCb in near future. In the wake of the recent measurement of $B_c\to
J/\psi\pi(K)$, $B_c\to J/\psi\pi(D_s)$, $B_c\to \pi(J/\psi,\psi(2S))$ and
$B_c\to J/\psi(\pi,\mu \nu)$ reported by the LHCb Collaborations, we predict
the ratios: ${\cal R}_{K/\pi}$, ${\cal R}_{D_s/\pi}$ and ${\cal
R}_{\psi(2S)/{J/\psi}}$ in broad agreement with the LHCb data though our
predicted ratio ${\cal R}_{\pi /{\mu\nu}}$ is found to be underestimated. The
results indicate that the present approach works well in the description of
exclusive nonleptonic $B_c$-decays within the framework of the RIQ model.
