We are having a private dinner reception after our wedding ceremony. Not everyone that attends the ceremony is invited to this private dinner reception. How should the response cards read?
It isn't polite to invite guests to the wedding and not the reception. It is like asking guests to the gift part of the event and telling them that they are not good enough to go to the party. This would only be proper if this was an 'open church' wedding in which all of the church members were invited. But, even then the church members would be invited to cake and refreshments.
Your guests to your reception would receive the standard response card. There is no polite way to state to keep quiet about the dinner.