Dendroid stony corals build highly complex colonies that develop from a single coral polyp sitting in a cup-like skeleton, called corallite, by asexual reproduction, resulting in a tree-like branching pattern of its skeleton. This dataset bundle contains computed tomography data of five coral colonies belonging to three reef-forming cold-water coral species: Lophelia pertusa (also known under the name Desmophyllum pertusum), Madrepora coulata and Goniocorella dumosa. For each colony the CT raw data (in DICOM format), the polyp cavity instance segmentation, the calices segmentation (given as unique label values) and a spreadsheet containing the (directed) edges of the colony skeleton graph (each label in the calices dataset represents a vertex in this graph; the edges are given by their start label Node ID #1 and the label of their target Node ID #2) are provided. This decomposition of dendroid coral colonies into their building stones (corallites with the respective calice) and subsequent determination of colony skeleton graphs provide the basis to study their ontogenetic development and morphoplasticity.