Hello Ann Marie,
"Voice-O-Graph" machines resembled phone booths and there were at least two dozen of them located in arcades all over Coney Island in the 1940s. The machines were manufactured by International Mutoscope. The company also made the Photomatic photo booths that printed black and white photos in a small metal frame. In the 1940s it would have cost 25 cents to record a record and a personalized label with your name on it was extra. You could sing a song or record a birthday message.
Your voice was recorded at 78 RPM, a technology that's hard to find today. The machines switched to 33 RPM in 1957 and some were still operating in Coney Island through the mid-1960s. Here is a picture of a record that was recorded at AmuseOMat arcade on Surf Avenue.
Would love to hear your recording!