Hover hints give "loved" as a definition of beliebt. I would say loved and beloved are interchangeable in English. I agree with EliE that beloved should be accepted. Or is "loved" not really a definition of beliebt?
you can be in a high school, and there's a really mean girl who everyone hates, but still everyone wants to be her friend because she throws great parties and has loads of money. She is popular but not loved or beloved.
Bethany, that's one example where popular means only "famous, well-known". But seeing as a famous person can be unpopular, we must conclude that popular can also only mean "liked, loved", rjjacob is right.
I would agree that beloved is a correct translation. In my written college level German text, beliebt is frequently used to mean beloved when referring to a place or tradition. Is it different if referring to a person?