I don't think so...looking back at 1968, 1952, etc. it appears that if the current occupant of the White House is generally regarded as unfavorable, his party has no chance of winning.
The only possible exception I can think of is 1856, but I don't know what Pierce's favorability ratings were. 1868 doesn't count (A. Johnson wasn't really a Republican).
The closest would be 1948.
Polling was only begun in 1936, however, so it's impossible to say how popular Presidents were before that other than by looking at the election results themselves.