The Star Trek: Deep Space Nine Technical Manual describes this vessel as an Excelsior級 starship variant, describing it as being among the ships "constructed from salvaged components, components in work, and custom assemblies fabricated by the individual fleet yards."
The episode "A Time to Stand" needed a shot of a retreating flotilla of Starfleet vessels. To beef out the scene, the production staff built several new ships, kitbashing them out of parts from commercially available AMT/Ertl-Star Trek model kits.
Among the kitbashes was the USS Buckner, which was referred to as the USS Centaur in a later scene of the episode, although a recent photo of the model still shows the original name. The model was not present in the opening flotilla scene, but was featured more prominently later in the episode. The Buckner was constructed from parts of the Reliant (no. 8766) and Excelsior (no. 6630) AMT/Ertl model kits. It was built by Adam Buckner, who still owns the model.  Buckner commented on his build, "The USS Buckner was a ship I built while at Paramount working on Star Trek: Deep Space Nine for a little boy who wanted a Star Trek ship. Gary Hutzel saw the ship and asked if it could be featured in one of his upcoming episodes. I let Gary use the ship. He added the green fluorescent tape for windows and the pink fluorescent paint for engines. As this ship would now be a shooting model, I produced a second model which I sent on to the boy as promised." 
As for the use of the fluorescent tape on the model Buckner explained, "The Paint and Tape were for work under UV lights (read "glow in the dark when struck with strong UV radiation"). We used UV for the matte process and some of the window and engine passes. By mixing the paint and selecting the appropriate tape color, the material would glow in a chosen color range, allowing the separation of windows, engines and mattes to different layers by selecting the desired color during transfer from 35mm film to digital, or in the compositing process." 
A somewhat redesigned CGI model of the Centaur was commissioned by Adam "Mojo" Lebowitz and built by Ed Giddings for use in various licensed print publications.  Lebowitz himself was responsible for the rendering of the model.  Orthographic views of this model were published in Star Trek Fact Files, no. 298, 2002 and Star Trek: The Magazine Volume 3, Issue 6.
- According to the novel Articles of the Federation, this type is the Centaur-class, making the USS Centaur the first of its type.
- Centaur is playable in Star Trek: Legacy. The player can command the ship in the TOS and TNG eras.
- The Centaur is also playable in Star Trek Online, where it is one of the three starting designs for Federation players' starships. It is on the same tier as (and interchangeable with) the Miranda and Shi'Kar classes.