Based on discussion that can be found at Wikipedia talk:WikiProject College football/Archive 23#Tree littering, in order for a biography article to contain a coaching tree list or section, that coaching tree's notablity must be established by multiple reliable third-party sources that explicitly discuss that coaching tree or that coach's legacy of mentoring disciples who then went on to become head coaches. Sources that merely report that X worked under Y do not suffice to establish the notability of a tree.
Repository for coaching trees that have been removed from articles due to lack of sourcing to establish notability below.