This is what I do for ornaments, and I don't see why it wouldn't work for a stocking. And, even if you just work it plain, it looks pretty cool.
Using the weave of the fabric to make the stitches even and in the same (mirror-imaged) positions on both pieces, work a chain stitch from the opening, around the stocking and back to the other side of the opening. Fudge around the curves if you have to, and don't work the opening; turn down a hem or nun's stitch it, and/or sew in a lining, after everything's put together. Clip and turn the edges to the back of the work and place the two stocking pieces together, right sides out. If you've been careful enough, the loops of the chain stitching should line up on the two pieces. Anchor a thread - and it doesn't have to match the chain stitching - at one end of the opening and whip the chain stitches together all the way around.
If the chain stitches didn't line up, use the same thread to whip, and fudge as you need to. As long as the fiber is the same, it won't be particularly visible unless you _really_ messed up.
You could also do double Cordovan lacing, which is sort of like Montenegran stitch and gives a braided effect, or you can whip the chain stitches twice (same or different fiber). Any fancy linear stitch (simple cross and all the long-arm cross variations, another chain stitch worked through the existing ones, double running through the chains in different fibers, Palestrina knots, etc., etc., etc.) can be used, in fact. Most of these will be stronger than just whipping once, and, as Phyllis said, have interesting embellishment possibilities, especially in the use of different fibers. And I very often add a bead at every second chain stitch, which creates a neat 'picot' edge.
HTH.
-- Emc^2