Another song may have been a precursor- "FARE THEE WELL."

The Chorus:

Fare thee well for I must leave thee,
But O! let not our parting grieve thee;
Happier days may yet be mine,
At least I wish them thine- believe me!

The verses are quite different from those of the 'tavern' song.

Bodleian Collection (19th c., no date range suggested).
2806 d.31(72)
Firth b.27(262)
Harding B11(1812)

The song "RADOO," posted earlier, is given the same aga range as "There Is a Tavern in the Town" by the Bodleian; 1877-1884.

Fuld, in his book of 'world-famous music,' says the first printing of "There Is a Tavern in the Town" is in William H. Hills, "Student Songs," 3rd Edition, copyrighted May 14, 1883, p. 8; the same as posted above by Jim Dixon.
James J. Fuld, 1866 and reprints, "The Book of World-Famous Music, Classical, Popular and Folk." P. 572.