There are two questions here to be answered, one of which has a new answer. The first is the origin of the concepts that make up modern ecological economics. The second, which has a new answer, is who first neologized the label:"ecological economics"?
Let me answer the second first. The term became widely know after the journal of that name, Ecological Economics, was founded in 1989 by the ecologist, Robert Costanza. Very briefly speaking, it has contrasted itself with "environmental economics," which is viewed as being based on conventional mainstream neoclassical economics, studying how to internalize externalities and also how to properly provide environmental public goods as studied in the "market failure" approach of economics. The general stance of ecological economics, which has numerous sub-branches that squabble much with each other (and which I am not going to get into here and now) views this as insufficient. It emphasizes needing to more clearly and explicitly incorporate both insights from and the modeling of ecology in connection with economics to emphasize and focus on the ecological foundations of economies, that real world economies are ultimately embedded within ecosystems, which are duly impacted by feedback from those economies. The journal has from the beginning claimed to take a "transdisciplinary" approach.
So, initially Costanza and those around him who founded the journal claimed to have coined the term, with it unclear which of that group initially did so, it more or less emerging from ongoing discussions. Some of those included Ann Marie Jansson (some have pointed to her as the originator), Carl Folke, Cutler Cleveland, and the more senior and well-known Herman Daly, among others. It supposedly arose around then, in the late 80s. But, I long knew they were wrong because I had been using the term for years prior to that period of time (the only one of those people I knew prior to then was Daly). But, I did not coin it and never have claimed to have done so.
Where did I get it? From the regional scientist, Walter Isard, who had served on the thesis committee at Penn of my major professor, Eugene Smolensky (with whom I studied at University of Wisconsin-Madison). In 1972, he published a book with four otherwise completely obscure coauthors whom I shall not list entitled _Ecologic-Economic Analysis for Regional Development_, New York: Free Press, which I bought a copy of at the time and read thoroughly. He proposed using an old standby of the old regional science, input-output analysis, to do this. The crucial idea was that in the I-O matrix one could essentially break it into four broad sub-matrices: an economy to economy one, an economy to ecology one (think pollution), an ecology to ecology one (Eugene Odum was already conceptualizing ecosystems as I-O systems, which species consumes which species), and ecology to economy (lots of stuff). Each sub-part could have lots of detail. I am not sure the precise phrase "ecological economics" appeared in that book, but it was pretty much there in the title, and from reading that book on, I thought in such terms.
The new news is that the term was used even earlier. A new paper in Ecological Economics, the December 2014 issue to be precise, by Qi Feng Lin, "Aldo Leopold's unrealized proposals to rethink economics," 108, pp. 104-114, identifies the famous forestry ecologist, professor of game and wildlife management, and father of the "land ethic" from the University of Wisconsin, which he coined in his most famous work (published posthumously in 1949), _A Sand County Almanac_ (for those in Madison, Leopold was also the father of the UW-Arboretum.). It turns out that at the very end of his life, when he was writing A Sand County Almanac, Leopold was indeed doing a broader rethinking of economics from a strongly ecological orientation, including drawing a diagram that looks like Quesnay's Tableau Economique could have done it of "food chains" that go from the natural world to the economic world. However, the bottom line on the phrase itself is that he wrote a memo to the University of Wisconsin administration in 1947 in which he proposed that there be a position created at the UW in, yes, "Ecological Economics." Given his untimely death not too long after, there was no action on this, and Leopold's memo remained obscure and unknown as near as I can tell until unearthed now by Lin.
So, what about the origins of the ideas of modern ecological economics? Well, I think the key here is in fact in what we see in Isard and Leopold, input-output analysis and its relatives. Indeed, the second paper in the journal, Ecological Economics in 1989, was a paper by Paul Christensen, "Historical roots for ecological economics - biophysical versus allocative approaches," 1(1), pp.17-36. Rather than going to the usual suspect, Malthus, he went to Quesnay and the physiocrats, with his Tableau Econoimique long being viewed as the fountainhead of input-output analysis, and certainly emphasizing land and nature as the foundation of the economy. That is probably the fundamental source, although most economists of that era and earlier wrote much about agriculture and its ecological foundations, with an even earlier candidate possibly being William Petty. As it is, I note that Herman Daly's first important publication was in the JPE (of all places) in 1973, a year after Isard et al's book, "Economics as a Life Science," essentially followed him by proposing at the aggregate level the quadripartite I-O approach that Isard and crew had already laid out the previous year. In any case, as sort of the older godfather of the Costanza group, Daly provides the crucial link between these earlier appearances of the concept and its full emergence at the end of the 1980s.