After traveling all over Amsterdam and visiting many jewelry shops, I finally found one that had my watch battery and change it while I waited! In a mere15 minutes I had what looked like a brand new watch. Apparently, most shops do not have a large selection of batteries or won't waste the time to change them, so it is difficult to find one that will, especially while you wait. The Battery Shop is conveniently located outside Central Station.
Location: Stationsplein 15, Amsterdam