The obvious explanation is that Robert LaFollette, the "Progressive" candidate, was their "favorite son", a Republican senator from Wisconsin. LaFollette considered himself the heir to the Theodore Roosevelt wing of the GOP, though TR had been dead for five years.
Coolidge was the incumbent in that election, having assumed the presidency after the unexpected death of Warren Harding.
John Davis, originally from West Virginia and who had moved to New York, was the last Democrat presidential nominee who could legimately be called a conservative. If you look at the map, the striking thing is that Davis swept all eleven states of the Old Confederacy, took Oklahoma (which, though it didn't enter the union until 40 years after the Civil War, was settled mostly by people from the Old Confederacy and their descendants), but won nowhere else. Coolidge had a massive 25 point lead over Davis in the popular vote nationally, a huge endorsement - except for the South - of his job performance in the one year and three months he had been in the White House.
This election is the subject of a book called The High Tide of American Conservatism, by Garland S. Tucker III, published by Emerald Book Co. in Austin, Texas in 2010.
Right on both counts, LaFollette won WI cause it was his home state, period, only reason, he won nothing else though he came in second well ahead of Davis in some western states. His was a newly formed Progressive Party, the TR 1912 party was already long dead.
Davis the last conservative rat to be nominated for President, but it’s hard to know how conservative he really was since people thought Wilson was a conservative democrat when he was the father of progressivism. Davis was certainly to the right of the wild haired LaFollette however.
Al Smith wasn’t so bad either, he turned against FDR and the new deal, might have been personal though since FDR beat him in 1932.