Here's the trick. Take three stud length 2x4s and nail them together floor to ceiling on either side of the room. Run a 2x4, cut to fit tightly, across the room and tight against the ceiling to fit snuggly between the jacks (the sets of nailed together 2x4's). Scew a block of wood to the floor, tightly against the bottom of both jacks. Now this next part can be a bit of a trick. You want to drill a 3/8 hole into the jacks towards the wall at the top and bottom, no more than 2 - 2 1/2 inches. Place a 3 inch drywall screw in each and tighten securely. Insert your eyebolts as needed and hang that hammock.
Now this was a rather grewsome and simple method, but you could dress the frame up up with paint or stain, do some routing, even use some decorative posts. In the end, it's your hang. As far as the hammock is concerned. My boys prefer a Wal Mart canvas painters drop cloth.