  We study a pair of commuting difference operators arising from the elliptic
solution of the dynamical Yang-Baxter equation of type C_2. The operators act
on the space of meromorphic functions on the weight space of sp(4,C). We show
that these operators can be identified with the system by van Diejen and by
Komori-Hikami with special parameters. It turns out that our case can be
related to the difference Lame operator (two-body Ruijsenaars operator) and
thereby we diagonalize the system on the finite dimensional space spanned by
the level one characters of the C_2^{(1)}-affine Lie algebra.
