Not sure what you mean by baby cs buckle. Never heard of a baby cs buckle, but that doesnt mean they dont exist.
Are you referring to size of buckle or the letters "cs"?
Your question did intrigue me though, so i looked in my copy of Plates and Buckles of the American Military 1795-1874 by Sydney Kerksis.
Most of the cs/csa plates i saw were on made of brass and copper and on average 2" x 3", give or take a couple tenths of inches in either direction.
There were several examples in the book where the lettering "cs" was much smaller than other ones.
One was similar to your avatar, but the lettering was about half the size. per page 293 dimensions 2.24" x 3.32". Brass.
Anyhow, Kerksis's book is 500+ pages, and full of illustrations. You can find it ebay for around 50 dollars used in good condition.