Dendroid stony corals build highly complex colonies that develop by asexual reproduction from a single coral polyp sitting in a cup-like exoskeleton, called corallite, resulting in a tree-like branching pattern of its exoskeleton. Despite their beauty and ecological importance as reef builders in tropical shallow-water and in huge cold-water coral mounds in the deep ocean, systematic studies investigating the ontogenetic morphological development of such coral colonies are largely missing. Two main reasons for this lack of study are the large number of corallites, and the existence of many secondary joints/coenosteal bridges in the ideally tree-like structure that make a reconstruction of the skeleton tree extremely tedious. Herein, we present CoDA, the Coral Dendroid structure Analyzer, a visual analytics toolkit that allows for the first time to systematically create skeleton trees representing the correct biological relationship of even very complex dendroid stony corals and to perform ontogenetic morphological analyses based on it. Starting with an initial instance segmentation of the calices/corallites, CoDA estimates the skeleton tree and provides convenient tools and visualizations for proofreading and correcting segmentation and skeleton tree. Part of CoDA is CoDA.Graph, a feature-rich link-and-brush user interface for showing the extracted morphological features and graph layouts of the skeleton tree, enabling real-time exploration of complex coral colonies and their building blocks, the individual corallites and branches. The use of CoDA is exemplified on multiple specimens of the three most important reef-building cold-water coral species with largely varying morphotypes.