We describe the design and operation of a high-stability Fabry-Pérot cavity, for laser stabilization in cavity quantum-electrodynamics experiments. Our design is based on an inexpensive and readily available uniaxial carbon-fiber reinforced polymer tube spacer, featuring an ultra-low thermal expansion coefficient. As a result, our 136 mm-long cavity, which has a finesse of 5160, shows a coefficient of thermal expansion of 1.6 × 10−6 K−1. Enclosing it in a hermetic chamber at room-pressure and using simple temperature stabilization, we observe absolute frequency excursions over a full day below 50 MHz for a laser operating at 446.785 THz. The frequency stability is limited by the imperfect thermal isolation from the environment and can be corrected using a built-in piezoelectric actuator. In addition, we discuss a different variant of this design and identify future improvements. Our system provides a cost-effective and robust solution for transferring laser stability over different wavelengths, as well as for linewidth reduction or spectral filtering of CW laser sources for applications in quantum science.