What brings more pleasure than swinging lightly in a shaded summer breeze? Not much. Maybe a small basketball (as see in the picture). But this need not be just a container for a hammock. Think of things you constantly bring in and out of your house, garage, shed and into your yard. Any of these things could fit into a custom made storage box and fitted to a tree in your yard (or to a 4x4 post set in concrete wherever you like). The two big uses for this kind of container that I can think of are for yard games and garden tools. If you and your family have one of those badmiton/volley ball sets, croquet sets, horsehoe sets or whatever then this might be a great storage solution for you. If you enjoy gardening then a well placed box with your shovels, hoes, and miscellany might be a time and energy saver. Could also be used to hold garden hoses, drip irrigation hoses, loads and loads of things.
You could also get dramatic and slant the post away from your tree, perhaps making the support even steadier. And then you could build your box on the "underneath" side, further protecting it from the weather.
I use eyebolts to hang my hammock and use carabiners ("real" ones) to attach to the eyebolts. If the distance isn't quite right, it's easy to put a double loop of rope through an eyebolt and tie off with a Double Fisherman's Bend.
One of my supports is my garage wall. In addition to the eyebolt screwed through the siding into a stud, I put another eyebolt ~5' away. My hammock lies flat against the garage wall when not in use hanging from both eyebolts, mostly protected from the weather by the eaves of the garage.
Or spread the two garage eyebolts further apart to get all the material tucked higher under the eaves. And then you could attach a horizontal box to the garage wall to stuff the -- oh heck, this is getting to be way too much work when I could be dozing in the hammock!
Okay, now where is your hammock weaving instructable? :-)