In the 1940s, Leroy Shaw wanted his son to have a good backyard toy he could share with the neighbors.

Armed with the skills of a motorcycle mechanic and sheet metal worker, he built a small train that could hold 24 kids.

More than 60 years later, Shaw and Sons Amusements still has the train, a humble reminder of the ride that sparked a family business. In its 64th year and third generation, the company has about 25 rides and 30 games.

"My son and daughter have been in it since high school and my nephew, and now my grandsons are coming along," said Ralph Shaw, Leroy's son and president of the Severn company, who will be...