In the design of graph theoretical models, the quantifiable parameters encountered in the process will be represented through qualitative characterization of mathematical, in particular, graph theoretical tools. Coloring and labeling techniques come in handy, in such representations of social, biological and physical data systems.In the proposed series of publication of AUM Block coloring, in volume 1, ¿New AUM Block Coloring technique for Corona Product of Graphs¿, the concept AUM Block coloring is introduced for corona product of path, Cycle, Complete graph, and Wheel graphs. This volume 2, focus on developing AUM Block coloring for special graphs such as Star graph, Double Star, Olive tree, Banana tree, Coconut tree, Bamboo tree, Tadpole graph, Lollipop graph. AUM Block Chromatic Number for these graphs is also found. This notable contribution will be very much helpful to the aspiring researchers in Mathematics and Applied fields. Such graph theoretical tools serve as solution providers to many real life, practical problems, in varied fields like communication network, data mining, web designing, image processing, agricultural crops plantation pattern etc.