An electronic device may have a display that is protected by a transparent cover layer. The transparent cover layer may include a laser-annealed sapphire coating on the outer surface of a glass substrate or other transparent substrate. The sapphire coating may provide the display with a hard, scratch-resistant outer surface. The sapphire coating may be formed by coating a glass substrate with a thin film of amorphous aluminum oxide. The aluminum oxide thin film may be locally heated to transform the amorphous aluminum oxide into alpha-phase aluminum oxide (sapphire). Local heating may be achieved by laser annealing the aluminum oxide coating with a carbon dioxide laser. The laser may produce laser light having a wavelength that is absorbed in the aluminum oxide coating without being absorbed by the glass substrate so that the glass substrate is not damaged during the laser annealing process.