Update:
This series was initially published on the club's website in June, 2015. Well, five years later a fourth set has finally been discovered - horses. Same design, height, and holes. These horses have gold and red "Relco Japan" stickers.
Horses
This series consists of three different wild animals. Each set has mosaic tiles decorating their exterior. Made in Japan. ca 1950s-60s. About 4.5 inches tall.
Deer
Giraffes
Elephants