ASTRI is a Flagship Project of the Italian Ministry of Education, University and Research, led by the Italian National Institute of Astrophysics, INAF. One of the main aims of the ASTRI Project is the design, construction and verification on-field of a dual mirror (2M) end-to-end prototype for the Small Size Telescope (SST) envisaged to become part of the Cherenkov Telescope Array. The ASTRI SST-2M prototype adopts the Schwarzschild-Couder design, and a camera based on SiPM (Silicon Photo Multiplier); it will be assembled at the INAF astronomical site of Serra La Nave on mount Etna (Catania, Italy) within mid 2014, and will start scientific validation phase soon after. The peculiarities of the optical design and of the SiPM bandpass pushed towards specifically optimized choices in terms of reflective coatings for both the primary and the secondary mirror. In particular, multi-layer dielectric coatings, capable of filtering out the large Night Sky Background contamination at wavelengths $λ \gtrsim 700$ nm have been developed and tested, as a solution for the primary mirrors. Due to the conformation of the ASTRI SST-2M camera, a reimaging system based on thin pyramidal light guides could be optionally integrated aiming to increase the fill factor. An anti-reflective coating optimized for a wide range of incident angles faraway from normality was specifically developed to enhance the UV-optical transparency of these elements. The issues, strategy, simulations and experimental results are thoroughly presented.