This depends on the material that the spare tire cover is made from. Most are made from heavy-duty vinyl that can be painted effectively with the right materials. If you are going to paint your spare tire cover, then take your time, ensure you plan out your design, and use the right materials for the best finish. Acrylic paints are ideal for this task and clear coat can be used to protect your design from the elements once it is finished.
Alternatively, find a professional artist that can create a unique design for you and who can airbrush the design onto your spare tire cover. When you contact the artist (or order your own airbrush set), be sure to have all the information on your cover including size and material. This will help you pick the right set.