Arkie: Check the ingeb.org website, a great German-based folk song site. If you search there for "zu Bethlehem geboren", you'll find several carols that include that phrase, including one by that title (by Friedrich von Spee), for which both a text and a MIDI are supplied. Other possibilities there, also with MIDIs:

Als ich bei meinen Schafen wacht = While shepherds watched their flocks*
Es kommt ein Schiff geladen (A laden ship comes)
Heilige Nacht** (Holy Night): "Geboren ward zu Bethlehem..." [No MIDI]

* The "While shepherds" setting with this chorus:
How great their joy! (Great their joy!)
Joy, joy, joy! (Joy, joy, joy!)
Glory to God in Heaven on high!
Glory to God in Heaven on high!

The melody in these MIDIS is carried by an interior voice; it is not readily apparent.

Also at ingeb.org is "Die Blümelein, sie schlafen", a song with a setting by Johannes Brahms based on "Zu Bethlehem geboren". The tune here is more distinct.

Please let us know if any of these is what you remember.