Does the Bible say if animals in Eden were carnivorous, or when animals on Earth became carnivorous? Do the canonical writings of any Christian group say if animals in Eden were carnivorous, or when animals on Earth became carnivorous?
The short answer is "yes, sort of".

The only sub-group within Christianity that I'm aware of that cares about whether the animals in the Garden of Eden were originally carnivorous or not are the Young Earth Creationists.  

To other groups, it's simply a non-issue.  Only within the young-earth paradigm do you get the idea that there was no physical death before Adam's sin, and thus it's only from that view that there's a necessity to explain what the animals ate before the fall.

Example of the YEC teaching on the subject can be found here.

Going further, understanding the YEC mindset, the only reason to believe in a young-earth creation as literal history is because of the belief that the Bible, including the first portion of Genesis, is meant to be taken literally.

The reason this is important is that the Bible is considered to be the only authoritative source of Truth, particularly among these groups.

So, to these groups, the only thing that can be considered "canon" is the Bible itself.

While the Bible doesn't use the word "herbivore", it does say this in Genesis 1:29-30:


  29 And God said, Behold, I have given you every herb bearing seed,
  which is upon the face of all the earth, and every tree, in the which
  is the fruit of a tree yielding seed; to you it shall be for meat.
  
  30 And to every beast of the earth, and to every fowl of the air, and
  to every thing that creepeth upon the earth, wherein there is life, I
  have given every green herb for meat: and it was so.


So, a literal interpretation of verse 30 implies that all living things were given plants to eat.  It doesn't exactly say "They can't eat meat", but it  does say that God has given plants to eat to every beast of the earth and fowl of the air - and every would include those that are carnivorous today.

Most YEC groups do take this to mean that originally all animals were herbivorous.

With that said, there are dozens of alternate ways that the genesis account is understood.  It could be just as easy to say that God gave them plants but that doesn't mean that it's ONLY plants that they were given. It could be that they were able to eat meat, but that just wasn't mentioned.  And of course, to anyone other than the YEC adherents, it's a non-issue.