As you can notice from the comments under your post, there is no such thing as a fallback but you always can find a way to solve the problem. Also keep in mind that sometimes when you come up with an unusual solution there is always be a price: performance, readability, etc.
For your situation I can suggest some ideas how you can solve that:
Use two images (those mustn't be transparent)
background-image: url("defaultImage.png"), url("backupImage.png"); background-position: 0 0, 0 0; background-repeat: no-repeat, no-repeat;
Use two nested HTML elements, for instance. Styling them and add background-image for both.
In css add pseudo elements through :before{content:" "; background:url(backup.png); display: block; position:absolute;}