  Given two newforms $f$ and $g$ of respective weights $k$ and $l$ with $k<l$,
Hida constructed a $p$-adic $L$-function interpolating the values of the Rankin
convolution of $f$ and $g$ in the critical strip $l \leq s \leq k$. However,
this construction works only if $f$ is an ordinary form. Using a method
developed by Panchishkin to construct $p$-adic $L$-function associated with
modular forms, we generalize this construction to the case where the slope of
$f$ is small.
