  Hirota's discrete KdV equation is an integrable partial difference equation
on $\mathbb{Z}^2$, which approaches the Korteweg-de Vries (KdV) equation in a
continuum limit. In this paper, we show that its multiplicative-discrete
versions have the special solutions given by the solutions of $q$-Painlev\'e
equations of types $A_J^{(1)}$ $(J=3,4,5,6)$.
