Well, three Presidents got married during their time in the White House: John Tyler, Grover Cleveland, and Woodrow Wilson. Tyler and Wilson both lost their first wives early in their Presidencies and remarried before they left office (Cleveland was a bachelor and his White House wedding was his first marriage), so they obviously were courting their second wives during that time. Tyler’s pre-marital relationship with his second wife, Julia, was much more private than Wilson’s was. Wilson and his second wife, Edith, went public with their relationship while they were dating, so I guess they would best fit the bill.