Pausanias (6.17.1) records that Damokrates' statue was made by Dionysikles of Miletos. According to Moretti (1957), no. 596 this sculptor was active in the late 3rd and early 2nd century BC. Hence, our dating: 225-175 BC. Moretti suggests that Damokrates' Olympic victory took place at the 144th Olympiad (= 204 BC).
IvO 39, ll. 28-30 (cf. SEG 57.396) records a certain Damokrates who received citizenship of Elis. Whether this indeed was our Damokrates, seems to me uncertain though. Moretti suggests that Damokrates might have been the brother of Polykrates, son of Hagetor, of Tenedos, who was victorious in wrestling at the Panatheneia in 190/189 BC (IG II-III(2), 2313, ll. 48-49). Also Aelian (V.H. 4.15) mentions a wrestler called Damokrates who won several victories in various disciplines. [DvdL]