The key to getting a side pull brake to stay centered is to get the pivot bolt centered and tight. You have the added challenge of getting the pivot bolt centered and getting the fender centered at the same time.
Here is a diagram so that we can get our language straight.
A - Rear pivot nut
B - Rear pivot nut washer
C - Rear pivot nut curved washer
D - Pivot bolt
Skipping a few parts...
N - Lock nut 1
O - Lock nut 2
Here is your picture with N-lock nut 1 and O-lock nut 2 marked.
A-rear pivot nut is hidden in this picture by the fork.
First - get your brake pads centered. I'm going to summarize a detailed article from Park Tool on centering a side pull brake.
- Snug up A-rear pivot nut. Tightening this nut will cause the
- D-pivot bolt to turn and it will cause the
- fender mount bracket to turn
Both your brake pads and fender will go off center.
Second - Get your lock nuts set.
The lock nuts provide the adjustment for the brake arms (G and I in the drawing). The brake arms should have as little front to back play as possible and still move freely. Once the brake arms have the proper amount of play tighten the two nuts against each other so they are locked in place.
Third - Get your D-pivot bolt centered.
The spring (E in the diagram) is what determines if the brake arms are centered. Turning the pivot bolt adjusts the center of both the spring and the brake arms.
Note: some brakes have a place on the pivot bolt for a thin wrench that allows for a one wrench pivot bolt adjustment. It would be located on the fat part of the pivot bolt where the spring attaches. If you don't have this keep reading.
Getting the pivot bolt to turn is a matter of putting a wrench on the A-rear pivot nut (usually a 10mm wrench) and a wrench on the correct lock nut and turning.
If the pivot bolt needs to turn clockwise you want to put your wrench on lock nut 2 so that it turns into lock nut 1.
If the pivot bolt needs to turn counter clockwise you want to put your wrench on lock nut 1 so that it turns into lock nut 2.
You should see the pivot bolt turn, which turns the springs, which turns the brake arms.
Picture of turning the pivot bolt
Note, in the picture the front wrench is on lock nut 1 so the mechanic is turning the pivot bolt counter clockwise.
Last - getting the fender straight
Holding the pivot bolt in place you want to shift the fender mounting brace so that the fender is centered on the tire/wheel.
Using an adjustable wrench you may be able to grab the fender mounting brace. Then, with your lock nut holding trick from step three, hold the pivot bolt in place and turn the adjustable wrench until the fender is in the right place.
This all sounds tricky and complicated but it gets easier with practice.