For an overview of the Liberty Party in the Taylor/Fillmore administration, see the first convention
of the four held by the Liberty Party in 1852.
The second Liberty Party convention of 1852 was called when the first convention was lightly attended.
The convention was held in a building called the Canastata in Syracuse NY on 9/2-3/1852.
On the first day of the convention, two separate resolutions were offered on the future of the party. Gerrit Smith offered a resolution recommending that the Liberty party nominate the Free Soil ticket of Hale and Julian. William Goodell offered a competing resolution calling for a separate Liberty Party nomination. On the second day, the convention voted for Smith's resolution by a margin of 17. At that point, Goodell's supporters bolted and held the third convention of the party in 1852.
After the bolt, the remaining delegates (apparently a majority of the whole) decided to postpone nominations until 10/1/1852, at which time the fourth convention of the Liberty Party for 1852 took place.