It would be great to check out the writing style if you take some photos or type in some of the text.
I did some Google searching and here’s what I found. (Hint: put quotes around search words to search on the phrases, i.e., “Charlotte Mason”.)
I found a mention of the book in a publication called The Dial, A Monthly Journal of Current Literature, Plublished by A. C. McClurg & Co., Chicago, May, 1888.
It was really a listing for another book but mentioned A Friend for Little Children.
Alma Ryan; or, Steadfast and True By Charlotte Mason, author of “A Friend for Little Children,” etc. 12mo pp. 256. Robt. Carter & Bros $1.25
I then searched on Alma Ryan and found more listings.
The American Bookseller, A semi-monthly journal, Jan-July 1889
Alma Ryan; or, Steadfast and True, is a pretty story of the life of a young girl, the daughter of the vicar of an English parish, who succeeded in making herself of great help to all around her, and whose life was as happy and bright as it was noble. It is by Charlotte Mason, who is a new but charming writer for girls, and will prove very widely popular. (Robert Carter & Bros.)
Book News, A monthly survey of general literature, Sept 1890 to Aug 1891
Alma Ryan; or, Steadfast and Trueby Charlotte MasonFrom the Closing-Out Sale of Robert Carter & Bros.
British books in print, J. Whitaker & Sons, A list of Walter Scott’s Publications, Sept 1888
By Charlotte MasonAlma Ryan; or, Steadfast and True
So, nothing conclusive but it might give you some more ideas to search. BTW, Sonya said that she checked timeline and the list of CM’s writings in The Story of Charlotte Mason, and neither mention it.