To me, restringing isn't really restoration as much as it is doll maintenance. Some dolls were strung with stringing cord that was a tube of cotton with a rubber core. Others were held together with a thick rubber band. Larger dolls had two connections. Arm to arm and then a second between the head and the legs. Over the years, the rubber perished. The arms and legs and head no longer will hold a pose and the doll needs to be propped up to be displayed. Replacing the cord is like restringing a guitar - not restoration; just good maintenance.

The doll in the example is a 13" Shirley Temple. The cord I'm using is 1/8" in diameter and because she's a fairly small doll, I'm only using one piece to join her head, arms and legs to the body.

You can order stringing cord in a heavy width for dolls larger than 14" and a thinner cord for 14" and smaller dolls from the ThisOldDoll shop by clicking here.
figure 1 Here's the project. Besides the arms, legs, body, and head, I've assembled the cord, needle nose pliers, a button hook, a piece of a large paper clip, and somehow, my scissors didn't get into the photo.
figure 2 Because there's no hook on the V shaped wire inside the doll's head, I used my pliers to make one out of that piece of paper clip. I've made nice looking ones, but this will do.
figure 3 First, I make a loop about 2/3 the size of the doll's body and tie a shqare knot as shown.
figure 4 Now pull the long end of the cord up and away from the loop.
figure 5 When I pull it so the cord until the knot turns, I have a slip knot. If this doesn't work, it's because my square knot is not tied properly.
figure 6 Now that I have a loop 2/3 the size of the doll tied with a slip knot, I put the hook on the loop and then onto the V wire in the doll's head. If there had been no wire in the doll's head, I'v have made made one from a coat hanger, making sure the V is up out of the way of the eye counterweight and that it doesn't put too much stress on the head. Inside the head are two dimples on the seam where the tops of the V should be. Happily, the V wire is still in this head so I just want to attach the cord to the V via the hook. Often I see people just tie the cord directly over the V wire. This is not good. It keeps the head from posing properly, so make a hook.
figure 7 Next I use the button hook up through one leg socket and out the neck to draw down the loop.
figure 8 Holding the loop with the button hook,
figure 09 I hook on the leg.
figure 10 Now I pull the loop out the other leg socket and hook on the other leg. It's important that the knot NOT be between the two leg hooks.
figure 11 Next I use the button hook to pull the loop out an arm socket and hook on an arm.
figure 12 And then on the other socket, the other arm.
figure 13 Now the doll is together but pretty loose. I use the button hook to get the knot out of the leg socket.
figure 14 Holding the knot, pull the long end up until the stringing is firm. I test this by posing the doll
figure 15 The stringing should be loose enough to let the doll sit easily.
figure 16 And tight enough to let the doll stand and pose her arms and head. If the stringing is too loose, she won't be able to hold up her arms or stand. If it's too tight, pressure on the joints will eventually split the head and the body, and the doll won't be able to sit (it's a good test).
figure 17 Once the slip knot has given me the right tension, it's necessary to tie one more knot over it to keep it from slipping out of position.
figure 18 Pull up the knot and tie the simple knot over the slip knot.
figure 19 And then tighten and clip the ends of the cord about 1" from the knot.
figure 20 Done!
figure 21 Since I string dolls this size often, I'm saving myself some future work by taking the pieces off the center loop and use it as a reference to make more of these for the future. This will save me from having to resize the loop on the next doll but since hooks and dolls vary, I might want to hold off on that final knot over the slip knot so I can easily adjust the tension for each doll.