The Chin'toka system's binary planets
Binary planets were a pair of planets that revolved around their shared center of mass while also sharing an orbit around their primary.
The planets Ni'Var and T'Khut in the Vulcan system formed a binary pair. They orbited the star 40 Eridani A. (SNW: "Charades")
The Chin'toka system's second and third planets were a binary pair. They themselves had at least two moons. (DS9: "Tears of the Prophets")
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While the term "binary planet" is not used in the episode, the two planets in "Tears of the Prophets" are referred to as such multiple times in the script. [1]
Romulus and Remus are not binary planets
Although Romulus and Remus are referred to as sister planets and appear remarkably close to each other, a computer graphic seen in Star Trek Nemesis shows them to have their own distinct orbits around the Romulan sun, meaning that they are not binary planets.
According to StarTrek.com, Tyrus VIIA was "one of a double planet" with Tyrus VII. [2](X)