The earliest reference I have found to a small ball park being a called a bandbox is from John Updike, who wrote in New Yorker magazine in 1960:
"Fenway Park is a little lyrical bandbox of a ballpark. Everything is painted green and seems in curiously sharp focus like the inside of an old fashioned Easter Egg. It was built in 1912 and rebuilt in 1934 and offers, as do most Boston artifacts, a compromise between man's Euclidean determinations and nature's beguiling irregularities."