Tennessee, Kentucky and Vermont
Missouri and Maine
48 (last of the contiguous states)
1889. North and South Dakota, Montana, and Washington become states
The last 2 states added to the Union were Alaska and Hawaii.
That could be Kentucky or Missouri, which both had three borders with free-soil states. But they had also stayed in the Union, as 'buffer states' that had voted against joining he Confederacy.
During James Buchanan's presidency, one state, Kansas, was admitted to the Union in 1861.
Oklahoma was granted statehood on November 16, 1907. It was the first of five new states added during the 20th century.
No states were added to the union while Pierce was president.
None of them did. There is a link below to a question about states that seceded in the 19th century.
Possibly
No states were added to the union while Van Buren was President.
Warren G. Harding served as President of the United States between 1921 and 1923. There were no US states added to the union between these two years.
States admitted in the 20th century: Oklahoma, New Mexico, Arizona, Alaska, and Hawaii.
Two states were added to the Union during Taft's term; New Mexico & Arizona.
Alaska, in 1959.
Missouri and Maine
The strength of the Union is what caused the three border states to remain in the Union. The states had to take a look at the fighting sides and decide which they felt would benefit them the most at the end of the war.