Thus far no one has mentioned the possibility the belt is past its time.
Belts can stretch a bit and if they become glazed they can slip. Perhaps trying a new notched belt (like
@SycloneDriver's) will solve the problem. The notches increase the contact on the pulleys and should reduce the tension needed to drive the alternator. Going down one belt size might also help.
The alternator appears to be the original alternator which is probably a 35a or 55a alternator. It should be easily driven by a belt that is new and not worn.Adding a larger washer, either a lock washer or a double thick fender washer, will also help maintain the tension. For an alternator this small there should be no need for a serpentine belt.
I actually found this not to be the case. While the standard adjusting bolt held the tension on a 90 a alternator, after changing to a 165a alternator and adding a serpentine belt the adjusting bolt could not maintain appropriate belt tension.