(Dictionary of American Regional English)
Chinese apple n
A pomegranate (Punica granatum).
1980 DARE File NYC (as of 1948), Chinese apple = pomegranate.
I didn't find evidence for this on Google, or the historical New York Times full text database, or the Newspaper Archive database of regional American newspapers.
The pomegranate juice drink is called POM in New York City as is it elsewhere.
Perhaps "Chinese apple" is historical; perhaps people once associated it with Chinatown; perhaps a few grocers had once chose this name to label the item. From my experience, it's a "pomegranate" here.