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Here's the plan: I'd secure one end to a tree with a simple evenk (Siberian) hitch, and the other end with a tarp-taut hitch. Along the length I'd place two marlin spike hitches which would act as stopper knots for a pair of carabiners which I'd then clip my hammock to.
I haven't tested this idea yet, and I'd like some feedback before I go off and trust my weight to it.
-Aduro
The problem I can see is if the carabiners are on the side closest to the tree, then the segment between the stoppers may not be under tension. This is not an issue unless you want the segment between the stoppers to act as a structural ridgeline. In this case the hammock should be fixed to the suspension line in such a way as to prevent the ends of the hammock from sliding either towards the tree or away from the tree. You could tie a couple of manharness or butterfly knots in the line as loops for the carabiners. This way the hammock ends will not move in either direction. The problem with that is the knots are in a fixed position and so you would have to centre the hammock by tying and retying at the trees. In Grizz's first video on hammock suspension he showed a single line suspension using descender rings. They allowed for much more adjustability.
Lots of good reading on related ideas await you, dating back a couple of years :D . I think the post that kicked it off was this one by HC4U. Search the forms (using either the "Search" function, or google using the site:hammockforums.net clue that limits the search to the named site) looking for SLS, or "Single Line Suspension".
happy reading!