Is there a way to override how DataContractJsonSerializer serializes Dates?

Well there is a workaround described here http://blogs.msdn.com/b/carlosfigueira/archive/2011/09/06/wcf-extensibility-serialization-callbacks.aspx under the topic "Fine-grained control of serialization format for primitives".

The main idea is to use a string backing field for the unserialized values and a property which performs serialzation and deserialzation in the setter and getter. That´s not ideal from the performance view but it could be a solution in some situations.

No, there's no hook in the serializer itself to do that. But you can use some of the serialization callbacks to implement this same behavior. You'd create another data member (of type string), and before the data is serialized, an [OnSerializing] callback would be invoked to copy the value of the DateTime field to the string one. The section "Fine-grained control of serialization format for primitives" in the post about serialization surrogates (at http://blogs.msdn.com/b/carlosfigueira/archive/2011/09/06/wcf-extensibility-serialization-callbacks.aspx) shows more details of what needs to be done.