Robert Burns music was already popular here in the colonies (he died in 1796) Also remember that songs were popular for a very long time and sometimes show up today as children's songs. (Misty Moisty morning, the frog and the mouse, fox went out on a chilly night all appear in Thomas Ravenscrofts collection circa 1609) Many broadsides used melodies that also appear as dance tunes so you could fit your lyrics to appropriate tunes found in dance tune collections.

good luck
Julia