As of 2152, Denobula was heavily populated, with twelve billion inhabitants on a single continent. The cities were quite crowded, though Phlox noted that the atmosphere was "vibrant, communal". The riverside nightclubs of the Kaybin District were known as meeting places to find intimate partners during the Denobulan mating season. (ENT: "Dear Doctor", "Doctor's Orders", "The Catwalk")
Denobula was mentioned in a hallucination Hoshi Sato experienced in mid-2152. She imagined asking Phlox if people on Denobula spoke about the dreamt-up figure Cyrus Ramsey, which Phlox then denied. (ENT: "Vanishing Point")
In reality, later the same year, Phlox requested information on Pa'nar Syndrome from Vulcan doctor Yuris, claiming it was on behalf of a colleague on Denobula studying thymic sclerosis. (ENT: "Stigma")
This planet was only mentioned in dialogue.
Depicting the planet in canon
Phlox actor John Billingsley imagined the Denobulan homeworld as a utopia, to the point of causing the Denobulans to become insular. "I mean, maybe it's so Eden-like [on Denobula]," he reckoned, "that it's like, 'Oh, what do I want to go out there for? I've got everything that I want right here.'" (Star Trek Monthly issue 95, p. 43)
Denobula was mentioned in voiceover dialogue that was scripted for ENT: "Dear Doctor" but not included in the final version of that episode; at one point, Phlox said that miners who had been assigned, along with him, to a Denobulan mining facility on Pree'nos had tried to make their compound as much like Denobula as they could (such as with "entertainment from home"), though that hadn't seemed right to him. The planet was likewise referred to once in the final draft script of ENT: "Detained" but not in the final edit of that installment.
Denobula was referenced once in a deleted scene from "E²", Phlox mentioning that he was looking forward to introducing nearly thirty new-found descendants of his (who were meanwhile aboard a version of Enterprise from an alternate timeline) to his wives on Denobula. (ENT Season 3 DVD & Blu-ray special features)
Denobula was also referenced in the final draft script of "Divergence", though not in the final version of that episode. In the script, a scene description stated, "Fond memories of Denobula give Phlox something to smile about, even in these dire surroundings."
Shortly before Star Trek: Enterprise was cancelled at the end of its fourth season, John Billingsley expressed an interest in viewing Denobula in the series, saying, "I would love to see a visit to Denobula." In fact, Manny Coto once stated that, if the series had gone into a fifth season, Enterprise would indeed have visited the planet. 
Details from reference works
According to the reference book Star Trek: Federation - The First 150 Years (p. 75), a Romulan force attacked Denobula and its orbiting spaceport in 2158. The ambush resulted in over three million casualties and intimidated Denobula, causing it to refrain from supporting the Coalition of Planets during the Earth-Romulan War.
According to Stellar Cartography: The Starfleet Reference Library ("Stellar Cartography" p. 13; "Federation Historical Highlights, 2161-2385"), while Denobula Prime was located in the Beta Quadrant, the Denobula Triaxa system was located in the Alpha Quadrant. The latter was a Federation member.