Steve Harper and Leeana Costa, hosts of the K-98.3 show on Long Island, posed the fake invitation and response on Thursday on their show's Facebook page, the Advocate reported.
"I do not believe in what you do and will not subject my innocent son to your 'lifestyle,'" the note read. "I'm sorry Sophia has to grow up this way."
On Friday, Harper and Costa apologized for creating the fake invitation and response. They said the radio station was not aware of their decision.
"We were attempting to spur a healthy discourse on a highly passionate topic, but we made a mistake by misleading our listeners into thinking that this specific situation actually existed," they wrote on Facebook.