Put on a pair of rubber gloves. Combine a solution of 1/4 cup of hydrochloric acid and 5 cups of water in a bucket. Dip a lint-free cloth in the mixture, and wipe down the couch to remove oils and deeply embedded dirt.
Take a scrap piece of leather that is the same color and type as your couch, and dab a bit of the stain on it. Examine the results. The results will tell you how well the leather absorbs the stain and whether you will have to apply one or two coats of if you should dilute the dye with a bit of solvent. Make any adjustments if necessary.
Remove all the cushions from the couch, and set them aside. Pour the dye into a small pan. Dip an ultra-soft, 3-inch nylon brush into the dye, and coat the front of the couch's back panel. Make smooth, uniform strokes with your brush, re-dipping into the dye when necessary. Be careful not to oversaturate any one area of the couch. Continue in this manner, and cover the backside of the couch's back panel, the arms and the cushions.
Dip a 2-inch trim brush into the dye, and cut in to the cracks and crevices of the leather couch. Allow all the dye to dry for 24 hours. Evaluate the leather, and decide if you want it to have a second, darker coat. Apply the second coat in the same manner, and allow it a full 24 hours to dry. Buff the leather with a soft cloth.