How did you check that the covers are not there and where did the other program store them?
In general: MP3tag can get the sam picture for several files if they belong to the same album.
Otherwise you have to treat each file individually.
In respect to accurateness: The album information would be vital to get the correct picture. Otherwise the track could come from the EP, album, live version, greatest hits, best of, charts compilation and so on.
You would have to find out what your player needs. There are numerous threads in the forum that deal with various players and their very specific needs to display pictures.
Here is a thread that guides you to use albumartdownloader as a tool in MP3tag: