You might find a few suitable tunes in my Canadian Tunebook. I agree with what others have said, namely that what would have been popular in that decade would be the popular songs of Britain and the U.S., especially those published in sheet music form for playing 'in the parlour'.
Though the following songs would not have been 'chart-toppers' in the 1860's, I suggest them for your pioneer village gig, because each is a song written during or prior to that decade about a place or event in Southern Ontario. Better still, each has a story behind it that you could relate to your audience, be it big or small. In effect, you would be singing history lessons!
- The Battle of the Windmill
- A Fenian Song
- The Old Piney Woods (a song relating to the underground railroad)
- Scarborough Settler's Lament
- When You and I Were Young, Maggie (Yes, the lyrics originate in Ontario... be sure to read the story behind the tune!
- Young Man From Canada
- Lost Jimmy Whelan may be another suitable tune, but I'll have to check my reference material. It may originate later than 1860. It certainly sounds> old, as its style is typical of an English ballad.