Green’s Dictionary of Slang

inferior, cheap or of poor quality.

1906		Atlantic Monthly Nov. 640: The serious painters whose work is found in exhibitions, and the despised ‘buckeye’ painter who paints for department stores.
1920		S. Lewis Main Street 137: The walls of Mrs Cass’s parlor were plastered with ‘hand-painted’ pictures, ‘buckeye’ pictures, of birch trees, news-boys [...] and church steeples on Christmas Eve.
1958		A. King Mine Enemy Grows Older (1959) 71: A smiling nurse, who had probably seen innumerable movies of such buckeye situations, held up a small bundle for my inspection.