I was looking around some more at past conventions after I posted yesterday about the 1968 Democratic convention and found on Google Book Search the complete proceedings of the 1876 Republican National Convention. The 1876 convention was held in Cincinnati and resulted in the nomination of Rutherford B. Hayes (who as you all know won the presidency after a very disputed election).
Hayes was first nominated by Edward Noyes of Ohio (Hayes was also from Ohio if you remember and a past governor of that state). You can read the speech - it is very laudatory, as expected. There were also several seconding speeches from other states. Other candidates (this link is for another site that summarizes from the nominees, but you can read all the nominating and seconding speeches in the original proceedings, of course) for the Republican ticket in 1876 were James Blaine, Benjamin Bristow, Roscoe Conkling, John Hartranft, Marshall Jewell, and Oliver Morton. It took to the seventh ballot for Hayes to get a majority and if you track the procedure (there is a complete state by state vote break down for each and every vote), you can see that Hayes only won on that ballot - he was significantly behind on all the others. Blaine was ahead through most of the proceedings, but as other candidates realized they had no chance, allegiances were switched and Hayes ended up with the nomination.