One of the sites listed on the page Brucie linked to, is BlueGrass West: Songs of the Carter Family, which I believe has a complete selection of Carter Family songs. I used their new search engine, and couldn't find a song woth both "ocean" and "cup" in it. Here are the "ocean" phrases I found:

• When the waves are rolling on the ocean...
• Where the sunset turns the ocean blue to gold...
• Fly across the ocean, birdie Fly across the deep, blue sea
• If I had a ship on the ocean / All laden and lined with pure gold
• The storms are on the ocean
  The storms are on the ocean
  The heavens may cease to be
  This world may lose its motion, love
  If I prove false to thee
  (the best-known Carter "ocean" song)

Good luck!
-Joe Offer-