Below is a less well-known method I used with success back in the old sidepull days.

1. Tighten the two pivot adjustment nuts against each other. Make sure the caliper still moves freely. Of course you should have already lubed the pivot.

2. To move the caliper clockwise (looking from the front of the brake) put a wrench on the outer pivot nut and another on the nut in back that mounts the brake to the frame. Carefully move the wrenches in unison clockwise to center. To move counterclockwise put one (thin) wrench on the back pivot nut. If the caliper does not want to move loosen the mounting nut 1/8 turn and try again. See the pic below for an example of the 2nd procedure.

Now that I look at your pic I'm realizing the other item I should mention is to make sure the cable housing section at the rear is neither too short nor too long, as that can throw off the centering. There should still be a slight curve when the brake is completely engaged.