"Jingle Bells" was written in the mid-19th century by James Pierpont. The song was copyrighted under the title "One Horse Open Sleigh" in 1857 while Pierpont was living in Savannah, Georgia, and its title was changed to "Jingle Bells" when the song was republished in 1859." (Snopes)---> Online Source.
Dreidel dreidel dreidel I made it out of clay. Dreidel dreidel dreidel, with dreidel I shall play. just kidding, I know that's a Hanukkah song.
Stille Nacht, Heilige Nacht (Silent Night). Though I'm certain I missed something in your question formulation as there are too many songs from that period to qualify...
Sorry about that, got caught up. Congratulations on this one. Jingle Bells is the only one from the 19th century that still makes a top chart.