The term is coined in section 10.4 "Toward Theoretical Cliodynamics?" in Historical Dynamics : Why States Rise and Fall by Peter Turchin, where he defines cliodynamics...
... by analogy with cliometrics. The term cliometrics was originally used for the new economic history in a rather derogatory sense (Williamson 1991), but now cliometrics is an accepted and mature direction within history. If we understand cliometrics in the general sense (that is, a focus on any quantitative data in history, not just economic ones), then it is an extremely valuable complementary discipline to the historical dynamics research program.
First encountered on Robert A. Freitas' web site, listed as one of his "other interests". He considers it similar to Isaac Asimov's notional field of Psychohistory from his Empire series.
See also cliometrics.