We had a thread on this in 2005 in soc.history.what-if. Here was one person's try:
George Washington 1789-1793 (VA)
Charles Carroll 1793-1797 (MD)
John Adams 1797-1801 (MA)
George Clinton 1801-1812 (NY)
John Gaillard 1812-1817 (SC)
William Crawford 1817-1825 (GA)
Henry Clay 1825-1829 (KY)
Andrew Jackson 1829-1837 (TN)
Thomas Benton 1837-1841 (MO)
Willie Mangum 1841-1845 (NC)
Levi Woodbury 1845-1849 (NH)
Zachary Taylor 1849-1850 (LA)
Thomas Ewing 1850-1853 (OH)
Lewis Cass 1853-1857 (MI)
James Buchanan 1857-1861 (PA)
Joseph Lane 1861-1865 (OR)
Abraham Lincoln 1865-1869 (IL)
Hannibal Hamlin 1869-1873 (ME)
Ambrose Burnside 1873-1881 (RI)
George McClellan 1881 (NJ)
Thomas Bayard 1881-1885 (DE)
George Edmunds 1885-1893 (VT)
Thomas Bayard 1893-1897 (DE)
William Allison 1897-1901 (IA)
Robert LaFollette 1901-1909 (WI)
Albert Beveridge 1909-1913 (IN)
John Burke 1913-1918 (ND)
John Davis 1918-1921 (WV)
Hiram Johnson 1921-1929 (CA)
Charles Curtis 1929-1933 (KS)
Thomas Walsh 1933 (MT)
John Garner 1933-1941 (TX)
Hugo Black 1941-1949 (AL)
Claude Pepper 1949-1953 (FL)
Harold Stassen (MN) 1953-1958
Prescott Bush (CT) 1958-1961
Henry Jackson (WA) 1961-1969
Winthrop Rockefeller (AR) 1969-1973
James Eastland (MS) 1973-1974
Hiram Fong (HI) 1974-1977
Frank Church (ID) 1977-1980
Mike Gravel (AK) 1980-1981
Paul Laxalt (NV) 1981
Sandra Day O'Connor (AZ) 1981-1989
Dick Cheney (WY) 1989-1991
Ken Kramer (CO) 1991-1993
Tom Daschle (SD) 1993-2001
Chuck Hagel (NE) 2001
Frank Keating (OK) 2001-2005
William Richardson (NM) 2005-
https://groups.google.com/d/msg/soc.history.what-if/wPVb-7Txl24/SPXcdPZqLq8J
There are a few problems with this, of course--for example, is the US really ready to elect a Catholic president (Charles Carroll) in 1792? Yet Alexander Hamilton stated his willingness to support him in the event Washington did not run for re-election.
https://books.google.com/books?id=eJlYAAAAMAAJ&pg=PA59