Composites with high elastic modulus, high specific stiffness, and ultra-low coefficient of thermal expansion (ppb/K-level) will likely be necessary for future ultra-stable optomechanical systems, such as space telescopes for high-contrast imaging. Carbon fiber reinforced polymers (CFRP) offer many favorable properties but suffer from instability due to moisture absorption and creep, and currently cannot cost-effectively achieve the 1-5 ppb/K coefficient of thermal expansion (CTE) required. New materials are desired with high elastic modulus, high specific stiffness, and ppb/K-level CTE. This paper presents three composite designs whose CTE is tunable by ablating material from one or more layers after fabrication and CTE metrology. Each composite design contains sapphire facesheets and a core material of fused silica, silicon carbide or Allvar® to achieve zero- and tunable-CTE. Finite element models reveal that each composite design exhibits CTE tunability of 200-800 ppb/K. The specific stiffness of the Sapphire-Allvar® composite design is around 60 GPa/(g/cc), whereas the others have lower specific stiffness < 20 GPa/(g/cc). These designs demonstrate the principle of tunable low- CTE materials that may have promise for future ultra-stable telescopes.