Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
It is not permissible to pay zakah to a da`wah radio station unless there is a dire need for it to protect the religiosity of young and adult Muslims.
Answering your question, Prof. Dr. Monzer Kahf, Professor of Islamic Finance and Economics at Qatar Faculty of Islamic Studies, states:
As a principle, the answer is NO on the ground that priority is to the poor and needy and that Da`wah activities are the responsibility of all Muslims which should not be charged to the poor alone by taking it from zakah.
However, there may be a special exception in circumstances where there is a serious aggression of the religiosity of young and adult Muslims and such ratio broadcasting help them be ware of such aggression. But these are rare and may be in certain localities only.
Almighty Allah knows best.