Emeralds are crystals of Beryl containing chromium and often iron as trace impurities. The chemical formula is Be3Al2(SiO3)6, Beryllium Aluminum Silicate. It is the presence of the impurities within and distorting the crystal structure that gives the wonderful green color.
Emerald crystals are comparatively easy to grow and the raw materials are in reasonably good supply – so I would say yes, emeralds are renewable.
Natural emeralds are a different story, which is why they are the second most valuable gemstone after diamonds. The finest emeralds are sourced from Colombia especially in the Mura and Cosquez mines but recently deposits have also been found in Zambia, Brazil, Russia and Pakistan. Natural emeralds are not renewable because their rate of formation is very slow.