  The problem of a Klein-Gordon particle moving in equal vector and scalar
Rosen-Morse-type potentials is solved in the framework of Feynman's path
integral approach. Explicit path integration leads to a closed form for the
radial Green's function associated with different shapes of the potentials. For
$q\leq -1$, and $\frac{1}{2\alpha }\ln \left\vert q\right\vert <r<+\infty $,
the energy equation and the corresponding wave functions are deduced for the
$l$ states using an appropriate approximation to the centrifugal potential
term. When $-1<q<0$ or $q>0$, it is shown that the quantization conditions for
the bound state energy levels $E_{n_{r}}$ are transcendental equations which
can be solved numerically. Three special cases such as the standard radial
Manning-Rosen potential $(\left\vert q\right\vert =1)$, the standard radial
Rosen-Morse potential $% (V_{2}\rightarrow -V_{2},q=1)$ and the radial Eckart
potential $% (V_{1}\rightarrow -V_{1},q=1)$ are also briefly discussed.
