  In this work, the strong coupling constants of the vertices $DDJ/\psi$,
$DD^{*}J/\psi$, $D^{*}D^{*}J/\psi$, $DD^{*}\eta_{c}$ and $D^{*}D^{*}\eta_{c}$
are calculated within the framework of the QCD sum rules. For each vertex, we
analyze the momentum dependence of the coupling constants by considering all
possible off-shell cases. In these analyses, we consider the contributions of
the vacuum condensate terms $\langle\overline{q}q\rangle$,
$\langle\overline{q}g_{s}\sigma Gq\rangle$, $\langle g_{s}^{2}G^{2}\rangle$,
$\langle f^{3}G^{3}\rangle$ and $\langle\overline{q}q\rangle\langle
g_{s}^{2}G^{2}\rangle$. Then, the momentum dependent coupling constants are
fitted into analytical functions $g(Q^2)$ and are extrapolated into time-like
regions. The values of strong coupling constants are obtained by using on-shell
conditions of the intermediate mesons($Q^2=-m^2$). The final results are as
follows, $g_{DDJ/\psi}=5.01^{+0.58}_{-0.16}$,
$g_{DD^{*}J/\psi}=3.55^{+0.20}_{-0.21}$GeV$^{-1}$,
$g_{D^{*}D^{*}J/\psi}=5.10^{+0.59}_{-0.43}$,
$g_{DD^{*}\eta_{c}}=3.68^{+0.39}_{-0.11}$ and
$g_{D^{*}D^{*}\eta_{c}}=4.87^{+0.42}_{-0.40}$GeV$^{-1}$.
