"There do not appear to be any comments to delete."
I see nothing wrong with that sentence. It explains what the issue is and informs the user that the comment cannot be deleted because it doesn't exist.
You could write that sentence any number of different ways, but I don't really see any advantages/disadvantages between any of the possible options really.
If it was a CMS I wrote, it would probably say something like this:
The comment you attempted to delete no longer exists. It may have been deleted by another administrator.
To answer the second half of your question, the only difference between the two snippets you provides is certainty. The first version does not state definitively that there are no comments, only that it appears that way. The second one states simply that there are none.
The sentence is grammatically correct.
However, the meaning may not be exactly what you have in mind. It means the same as:
Apparently, there are not any comments to delete, or you selected ...
If your application knows that there are no comments to delete, then there's no need to say "apparently" nor "appear to be". Moreover, it can confuse the user.
And if the system is displaying "appear to be" because users may get the message in two conditions (1. no comments to delete and 2. other admin deleted the selected comments), then it should actually display two separate messages depending on the condition:
There are not any comments to delete.
Another administrator has already deleted the selected comment.