Seven times, the Presidential Inauguration Day has been on a Sunday, but all were conducted publicly on the following Monday.
These were as follows:
James Monroe—1821
Zachary Taylor—1849
Rutherford B. Hayes—1877
Woodrow Wilson—1917
Dwight D. Eisenhower—1957
Ronald Reagan—1985
Barack Obama—2013
All were sworn in privately on Inauguration Day, except Monroe, in his second term, and Taylor, who refused an earlier swearing in on principle, therefore, technically making Senate President Pro Tempore David Rice Atchison of Kansas technical “President” for 24 hours, although most of that Sunday, Atchison was sleeping, and made no decisions worthy of mention!
Of course, the first four Presidents who had a Sunday inauguration were on March 4, while Eisenhower, Reagan and Obama had it on January 20.