What is the ruling on saying "Ameen" when one of the shaykhs supplicates on a television program?

Saying "Ameen" to a supplication is permissible, whether the supplicant is near or far. It is prescribed for whoever hears the supplication and wishes to be among those included in it to say: "Ameen," meaning: "O Allah, grant it."

However, it is not permissible to say "Ameen" after a recorded supplication, because saying "Ameen" is an act of worship prescribed only for the supplication of a present supplicant. There is no real person supplicating in a recording.