  We consider one-dimensional elliptic Ruijsenaars model of type $BC_1$. It is
given by a three-term difference Schr\"odinger operator $L$ containing 8
coupling constants. We show that when all coupling constants are integers, $L$
has meromorphic eigenfunctions expressed by a variant of Bethe ansatz. This
result generalizes the Bethe ansatz formulas known in the $A_1$-case.
