OK, so if what you meant is that you want a specific overall background image on all single post pages of a specific category, this could prove non trivial.
There is a manual way to do it by adding the CSS rule below in Advanced Options > Head Section > Custom CSS Rule box, but you need to add a new selector for each post with the proper post id
.postid-xxxx, postid-yyyy, postid-zzzz {background:url(ImageUrl) no-repeat;background-size:cover;}
There may be a way to do that with an Action & filter, but @weaver would have to let us know if that is indeed possible.