If the center hole in the pulley doesn't fit the snout of the water pump, (too big) it's possible the PO has installed an incorrect pulley. If so, you'll need to make a bushing that allows the pulley to center up on the shaft. It doesn't even have to be metal- - - -a piece of PVC pipe or some other type of plastic could be used if you don't have metalworking equipment handy. It just has to be a snug fit on the pump shaft on the inside, and reasonably close to the hole size of the pulley on the outside diameter.
Jerry

"It is better to be silent and be thought a fool than to speak and eliminate all doubt!" - Abraham Lincoln
Cringe and wail in fear, Eloi- - - - -we Morlocks are on the hunt!
There is nothing noble in being superior to your fellow man; true nobility is being superior to your former self. - Ernest Hemingway
Love your enemies and drive 'em nuts!