To my knowledge the most contentious US election pre-20 year rule was the election in 1876 between Samuel Tilden and Rutherford B. Hayes: https://en.m.wikipedia.org/wiki/United_States_presidential_election,_1876
Tilden won the popular vote, but 20 votes in the electoral college (enough to swing the vote to Hayes) were in contention. The bulk of these votes were in the former confederate south which was still occupied after the civil war by union troops but where pro-Democratic Party militant groups sought to suppress the black vote: https://en.m.wikipedia.org/wiki/Mississippi_Plan
In the end, the election was decided in the proverbial smoke filled room. No one knows who the legitimate winner of the election was, but in exchange for the Democrats ceding the election to Hayes, the Republicans agreed to end Southern Reconstruction: