The nuclear relaxation behavior in s-wave superconductors has been investigated as for Chevrel-phase superconductors, TlMo6Se7.5 and Sn1.1Mo6Se7.5 with T(c) = 12.2 K and 4.2 K, respectively. The nuclear-spin-lattice-relaxation rate, 1/T1, of Sn-119 in Sn1.1Mo6Se7.5 reveals a distinct coherence peak just below T(c), followed by an exponential decrease with the isotropic energy gap of 2DELTA = 3.6 k(B) T(c) in a weak coupling regime. By contrast, 1/T1 of Tl-205 in TlMo6Se7.5 possesses no coherence peak, although the exponential decrease of 1/T1 has also been observed with a somewhat larger value of 2DELTA = 4.5 k(B) T(c) in a strong coupling regime. The stronger electron-phonon coupling enhances the superconducting transition temperature and at the same time, opens a decay channel to cause an intense damping of quasiparticles, resulting in the depression of the coherence peak. The comparison with high-T(c) superconductors will be discussed.