Barcelona lost the vote choice for the 1936 Olimpic Games because it was held on April 26, 1931, 12 days after the proclamation of the Second Spanish Republic.
If the Spanish political crisis after the end of the dictatorship of General Miguel Primo de Rivera -father of Jose Antonio Primo de Rivera, leader of Falangism during Second Spanish Republic- would have triggered an effective democratization of the Spanish monarchy (probably with the abdication of Alfonso XIII) or if the Spanish municipal elections of April 12, 1931 had been held in May, or the process hadn't triggered the repeal of economic policy made by the previous dictatorship -which had conducted an economic policy that today call Keynesian-, it is likely that Barcelona had won the choice, in view of the German internal situation at the date of the election.
However, to effectively prevent the outbreak of the Spanish Civil War, the only truly viable solution would have been for the victory of the Popular Front did not occur, by the previous victory of a coalition of all the Republican parties (whether of the left, center and right) who won in the second legislative elections, which were held in 1933 OTL. Thus, many facts that led to the Spanish political radicalization in 1936 would be avoided.