The Michigan County Histories and Atlases Collection at the University of Michigan (accessible here: https://quod.lib.umich.edu/m/micounty/ ) contains county histories published in the late 19th century and up until 1923. These histories tend to focus on the first years of European settlement and on, and they contain many mentions of fiddling. Scattered throughout the 428 titles in the above collection are mentions of particular fiddle tunes and/or dances. Below is that list. This is not an attempt at making any kind of definitive statement that these were the most common tunes or even tunes that everyone would know in 19th century Michigan. This is just a list of those that wound up being mentioned in the county histories.
These tunes are in no particular order except that Money Musk is the most commonly mentioned tune in the county histories. Some dances were also mentioned, although in certain instances it can be difficult to differentiate whether the names are tune names or dance names.
Money Musk
French Four (is a dance but there may also be a tune named this, seen in another 19th century collection).
Opera Reel
Old Zip Coon
Turkey in the Straw (typically same tune as Old Zip Coon)
Molly Put The Kettle On
Speed the Plow
Durang’s Hornpipe
Virginia Reel (can be a dance or a tune)
McDonald’s Reel
Irish Washerwoman
Fisher’s Hornpipe
Washington’s Grand March
Webster’s Quick Step
President’s March
Rogue’s March
LaFayette’s Grand March
Come, Haste to the Wedding
Naval Quick Step
Gilderoy
Ms McLoud’s Reel
Arkansas Traveler
Dances:
the Scotch Reel,
Lady Washington,
Sicilian Circles,
Hunt-the-grey-fox (might be a tune)
Pillow Dance (might be a tune)