Did not have a lot of luck. Nearly one year seems insane. If Obama gets his nominee on he will be the first President since Reagan to have more than two.

One guy on Twitter says 125 days.

https://twitter.com/studentactivism/status/698632681245044736

Here is the document he referenced. Brandeis took 125 days. The Republicans are basically saying it will be a year and a half at the minimum. Not sure how the country will react to that.

http://www.au.af.mil/au/awc/awcgate/crs/rl33225.pdf

Tyler's second seat was the longest vacancy.

http://www.cqpress.com/incontext/SupremeCourt/congressional_pressure.htm

Smith Thompson died Dec. 18th, 1843 and Samuel Nelson came on the Supreme Court on Feb. 14, 1845.

Several lame duck Presidents never got nominations through.
Other lame-duck presidents whose nominees were rejected include John Quincy Adams, Millard Fillmore, James Buchanan, and Lyndon B. Johnson.

There was a seat that remained vacant for the last two years of his presidency (Henry Baldwin died in 1844, and his successor Robert Cooper Grier was confirmed a year after Polk took office in 1846).

https://en.wikipedia.org/wiki/John_Tyler#Judicial_appointments

during the Tyler Presidency. But alas, no link, but a @Somebody.

[link:https://books.google.com/books?id=ktR1AwAAQBAJ&pg=PA51&lpg=PA51&dq=Longest+vacancy+on+the+U.S.+supreme+court&source=bl&ots=NDZq88R3PR&sig=u1hJg-3DYTFPJWVbw4Rf6NrzK4A&hl=en&sa=X&ved=0ahUKEwi_jImP9_XKAhVS-mMKHSPgC8YQ6AEIeTAN#v=onepage&q=Longest%20vacancy%20on%20the%20U.S.%20supreme%20court&f=false|

a guy who wasn't even elected over 150 years ago.