Nettie Lightfoot Series

Published by Wm. Carter & Bro.
1. Alphabet and Picture Book by Anonymous
2. Lessons for Children by Anna Letitia Aikin Barbauld
3. Mrs. Barbauld's Stories by Mrs. Barbauld
4. Little Marrian by Mrs. Barbauld
5. Little Thomas by Mrs. Barbauld
6. Useful Little Stories by Mrs. Barbauld
7. Willy, or the Happy Day by Unknown
8. Lazy Lawrence by Maria Edgeworth
9. Waste Not, Want Not by Maria Edgeworth
10. Little Poems by Mrs. O. W. Scott
11. Floweret by Mrs. Hughs
12. Little Tot's Book by Unknown

Wm. Carter & Bro. published these titles while it was at 7 Water Street (1861-1863).
Six of the twelve titles made up “Aunt Mary’s Library for Young Children”. Those six books and the six others listed here comprised the Nettie Lightfoot Series which was published by Degen, Estes & Co., Lee & Shepard, Charles E. Brown, Cobb, Andrews & Co., and George R. Dana & Co. Unlike those other publishers, I cannot find any reference that indicates that Wm. Carter & Bro. published a series called the "Nettie Lightfoot Series" although it did publish all of the titles which made up the series.

So I suspect that this group of books is the Nettie Lightfoot Series but cannot be certain.