I just hang mine from a tree when the weather's good, and from the hammock itself when it's rainy. obviously, depending on the tarp i'm using, there will be more or less coverage at the ends, so sometimes you have to make a loop of cord, tie it around the ridgeline, and clip the biner to it, further in under the hammock. hope that makes sense.
alternately, you can made a crude rack to set on the ground (couple rocks or logs as a base, with a few more sticks on top to lay your pack on) under the tarp.
i've also just taken a garbage bag and poked a small hole in the bottom, hung it over my pack (like a dry cleaning bag), and pulled a biner (attached to the carry loop) through the hole to hang it off my hammock's tieout straps. (I use that method when i have to bear bag it.)