A rocking chair was type of chair that was capable of rocking forward and backwards.
An old man sitting in a rocking chair, smoking a pipe, was part of Reginald Barclay and Alexander Rozhenko Ancient West holoprogram. (TNG: "A Fistful of Datas")
A Q who appeared as an old man sitting in a rocking chair, while also smoking a pipe, appeared in the version of the Q Continuum demonstrated by Q and Quinn to Kathryn Janeway and Tuvok in 2372. (VOY: "Death Wish")
Benjamin Sisko once claimed to Kasidy Yates that his great-great-grandfather had false teeth that he kept in a glass next to his rocking chair, and Yates made a similar prediction about Sisko "sitting in your rocking chair, watching the sunset over the mountains every night," from his proposed house in the Kendra Province. (DS9: "Penumbra")