Absorbable stents and absorbable stent coatings have been developed with improved properties. These devices preferably comprise biocompatible copolymers or homopolymers of 4-hydroxybutyrate, and optionally poly-L-lactic acid and other absorbable polymers and additives. Compositions of these materials can be used to make absorbable stents that provide advantageous radial strengths, resistance to recoil and creep, can be plastically expanded on a balloon catheter, and can be deployed rapidly in vivo. Stent coatings derived from these materials provide biocompatible, uniform coatings that are ductile, and can be expanded without the coating cracking and/or delarmnating and can be used as a coating matrix for drug incorporation.