Well, in 1920 we had Warren Harding(R-OH)/Calvin Coolidge(R-MA) and James Cox(D-OH)/Franklin D. Roosevelt(D-NY), so we're halfway there already. Nicholas Murray Butler(R-NY) also ran for President that year, perhaps he could be brought on with Harding. Of course, Harding seemed to prefer running with Sen. Irvine Lenroot(R-WI), and I can't see Butler being so in demand by 1920, even if he was the "replacement" VP in 1912. The solution there One Democratic candidate from Wisconsin is Joseph E. Davies(D-WI) who was the first chairman of the Federal Trade Commission. Davies served from 1915-16 until Pres. Woodrow Wilson asked him to run for U.S. Senate against, you guessed it, Irvine Lenroot.
The easiest way I can see to have the Ohio/Wisconsin ticket work is to keep Lenroot in the Senate and have him beat someone else in the 1918 special election, and keep Davies as the Chairman of the FTC; because if they intersect before the 1920 election; someone ends up as a loser.
So those are two potential options right there:
Warren Harding(R-OH)/Nicholas Murray Butler(R-NY) and James Cox(D-OH)/Franklin D. Roosevelt(D-NY)
Warren Harding(R-OH)/Irvine Lenroot(R-WI) and James Cox(D-OH)/Joseph E. Davies(D-WI)
Also, in response to the OP, here's an unlikely idea, but I'll throw it out anyway:
Thomas Dewey(R-NY)/John W. Bricker(R-OH) and Pres. Franklin Roosevelt(D-NY)/Fmr. Gov. James Cox(D-OH)
The big issue with this one is that Henry Wallace was booted off precisely because most people didn't think FDR had another term in him, so replacing the ill 62-year old President with a man in his 70s probably won't go over well.