It looks like many volumes of Confederate Veteran are online in their entirety at the Internet Archives. I periodically go back to both Google Books and the Internet Archive from time to time to see what has been newly posted, but I’ve been lax lately in that regard. It looks like most of these were uploaded in 2011. Confederate Veteran was published from 1893 to 1932, focusing mainly on the happenings of Confederate Veteran organizations. In many ways it is the Confederate counterpart to Union veterans’ newspaper The National Tribune. I’m currently working my way through the Tribune looking for articles on the Siege of Petersburg. I’ll be doing the same for the Confederate Veteran.
Note: So far I can’t find anything past Volume 31, from 1923. If anyone knows of later issues, please leave a comment here and I’ll update this post.