Gather tools. Remove chair pad screws with cordless screw gun. Remove corner blocks -- tap out with rubber mallet if glued. Take apart loose joints with rubber mallet. Wood shrinks over time and this aging process weakens the joints. Be sure to take care when removing the corner blocks and joints.
Start with a small pilot hole and use larger bit. Cut dowel pin off with a coping saw flush to surface. Mark the center of the pin. Drill pilot hold down through pin (Image 1) but not into chair frame. Match drill bit to the diameter of the dowel hole. Drill old dowel out. Check that the new dowel pin is nice and snug. Apply small amount of wood glue to nail and run around inside of hole. Apply glue to half of the dowel pin and tap it in gently with mallet. If new pin is too long, set old dowel pin next to it, mark length (Image 2) and cut off excess with coping saw.
Spread glue around joints with finger -- spread inside hold and around dowel pins, tape piece into place. Glue both male and female pieces to create the strongest of bonds. Repeat gluing process for all joints. It's better to use too much glue than not enough. You can always wipe off the excess. If you use too little glue, you may end up with a joint that was just as weak as before.
Use a strap clamp to hold frame together by putting a strap over the chair and around the rails of the body of the chair and adjust and ratchet until it's good and snug. You can also use a rope or an old belt, but a strap with a clamp works best. Glue and screw corner blocks back on by applying glue to the face of the rail and block with counter sunk side face-down, screw securely in place and wipe the excess glue with a damp rag.
Don't forget to use the numbers that you wrote on the pieces to put everything back into its proper position. Leave the chair clamped for at least four hours. Use a touch-up stain stick to repair small nicks and scratches on the wood. When using a stain stick, start with the lighter shades first, and then progress to the darker shades.