The title is something like “ The Little Brown Bunny”. The hardcover was greenish with a brown bunny on it toward the bottom center of front cover. It was from the 1960’s or possibly from the later 1950’s. My mother said it was NOT a Golden Book. The bunny on the front cover was possibly sleeping. The cover was mostly a soft light green. (We think.)
Stump the Bookseller
New format, same book stumper solving.
The Happy Place by Ludwig Bemelmans? https://www.goodreads.com/book/show/6411411-the-happy-place
Possibly The Velveteen Rabbit, originally published in the 1920s but reprint many times.
Maybe The Golden Egg Book by Margaret Wise Brown? Despite the title, it has a sleepy bunny on the front, surrounded by greenery. (Or, at least the version I have does).
It could be “Fussbunny” by Helen & Alf Evers. I am looking at it now. It has a green cover with a large brown bunny in the middle, sitting upright. It is not a golden book, though it is similar in size and shape. It was published in 1944 by Rand McNally & Company, though i read it growing up in the mid-50’s.