Oddball size so what is the brand of headset being used here?11/64" bearings are classed as 4.37mm (actually they're 4.365mm) and are readily available. Well, for a given value of 'readily' - you'll be unlikely to find them in a LBS or hardware store but any bearing supplier should have them.
I'd be curious as to what headset they fit in as it's not a size I've ever seen used.